Research output

Research output per year 2010 2012 2013 2014 2015 2017 2019 2021 2023

• 24 Article
• 19 Conference contribution
• 3 Chapter
• 2 Paper
• 2 More
  • 1 Editorial
  • 1 Review article

Research output per year

Research output per year

Search results

• 2023

  A generalised distributed-order Maxwell model

  Ferrás, L. L., Morgado, M. L. & Rebelo, M., 15 Jan 2023, In: Mathematical Methods in the Applied Sciences. 46, 1, p. 368-387 20 p.

  Research output: Contribution to journal › Article › peer-review

  • Viscoelastic Model 100%
  • Weighting Function 59%
  • Modulus 40%
  • Complex Fluids 36%
  • Fractional 34%
• 2022

  A spectral approach to non-linear weakly singular fractional integro-differential equations

  Faghih, A. & Rebelo, M., Dec 2022, (Accepted/In press) In: Fractional Calculus and Applied Analysis.

  Research output: Contribution to journal › Article › peer-review

  • Integrodifferential equations 100%
  • Galerkin methods 78%
  • Integro-differential Equation 63%
  • Numerical methods 61%
  • Nonlinear systems 58%

• Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations

  Morgado, M. L., Rebelo, M. & Ferrás, L. L., 2022, Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21) . Dzielinski, A., Sierociuk, D. & Ostalczyk, P. (eds.). Cham: Springer, p. 239-244 6 p. (Lecture Notes in Networks and Systems; vol. 452).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
• 2021

  A distributed order viscoelastic model for small deformations

  Ferrás, L., Morgado, M. L. & Rebelo, M., 2021, SYMCOMP 2021 – 5^th International Conference on Numerical and Symbolic Computation: Developments and Applications: Proceedings. Lisboa: APMTAC – Associação Portuguesa de Mecânica Teórica, Aplicada e Computacional, p. 179-197 19 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

• A Numerical Method for the Transient Couette Flow of a Distributed-Order Viscoelastic Fluid

  Ferrás, L. L., Morgado, M. L. & Rebelo, M., 2021, Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings. Gervasi, O., Murgante, B., Misra, S., Garau, C., Blečić, I., Taniar, D., Apduhan, B. O., Rocha, A. M., Tarantino, E. & Torre, C. M. (eds.). Cham: Springer, p. 411-421 11 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 12952 LNCS).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  • Transient Flow 100%
  • Couette Flow 94%
  • Viscoelastic Fluid 86%
  • Relaxation 64%
  • Differential equations 61%

• A study on mixed electro-osmotic/pressure-driven microchannel flows of a generalised Phan-Thien–Tanner fluid

  Ribau, A. M., Ferrás, L. L., Morgado, M. L., Rebelo, M., Alves, M. A., Pinho, F. T. & Afonso, A. M., Apr 2021, In: Journal of Engineering Mathematics. 127, 1, 7.

  Research output: Contribution to journal › Article › peer-review

  • Microchannel 100%
  • Microchannels 65%
  • Fluid 46%
  • Fluids 38%
  • Dimensionless 27%
  3 Citations (Scopus)

• High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations

  Ferrás, L. L., Ford, N., Morgado, M. L. & Rebelo, M., Dec 2021, In: Mathematics in Computer Science.

  Research output: Contribution to journal › Article › peer-review

  • Fractional Diffusion Equation 100%
  • High-order Methods 99%
  • Ordinary differential equations 92%
  • Fractional Differential Equation 80%
  • Numerical methods 76%
  1 Citation (Scopus)

• Stable and convergent finite difference schemes on nonuniformtime meshes for distributed-order diffusion equations

  Morgado, M. L., Rebelo, M. & Ferrás, L. L., 18 Aug 2021, In: Mathematics. 9, 16, 1975.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Convergence of numerical methods 100%
  • Finite Difference Scheme 77%
  • Diffusion equation 75%
  • Numerical methods 71%
  • Mesh 63%
  1 Downloads (Pure)
• 2020

  Analytical and numerical studies for slip flows of a generalised Phan-Thien–Tanner fluid

  Ribau, Â. M., Ferrás, L. L., Morgado, M. L., Rebelo, M. & Afonso, A. M., 1 Mar 2020, In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 100, 3, e201900183.

  Research output: Contribution to journal › Article › peer-review

  • Slip Flow 100%
  • Numerical Study 59%
  • Fluid 47%
  • Complex Fluids 46%
  • Viscoelastic Model 43%
  5 Citations (Scopus)

• Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces

  Morgado, M. L. & Rebelo, M., 2020, Differential and Difference Equations with Applications, ICDDEA 2019. Pinelas, S., Pinelas, S., Graef, J. R., Hilger, S., Kloeden, P. & Schinas, C. (eds.). Cham: Springer, p. 467-479 13 p. (Springer Proceedings in Mathematics and Statistics; vol. 333).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  • Collocation 100%
  • Fractional Differential Equation 93%
  • Fractional Diffusion Equation 58%
  • Initial Value Problem 42%
  • Numerical Examples 31%
• 2019

  A generalised Phan–Thien—Tanner model

  Ferrás, L. L., Morgado, M. L., Rebelo, M., McKinley, G. H. & Afonso, A. M., 1 Jul 2019, In: Journal of Non-Newtonian Fluid Mechanics. 269, p. 88-99 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Shear 100%
  • Flexibility 87%
  • Polymer Melts 58%
  • Polymer Solution 53%
  • Polymer melts 49%
  23 Citations (Scopus)

• A hybrid numerical scheme for fractional-order systems

  Ferrás, L. L., Ford, N. J., Morgado, M. L. & Rebelo, M., 1 Jan 2019, Innovation, Engineering and Entrepreneurship. Veiga, G., Machado, J. & Soares, F. (eds.). Springer Verlag, p. 735-742 8 p. (Lecture Notes in Electrical Engineering; vol. 505).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  • Differential equations 100%
  • Numerical methods 99%
  • Polynomials 86%
  • Networks (circuits) 61%
  2 Citations (Scopus)

• Black-Scholes Equation with Distributed Order in Time

  Morgado, M. L. & Rebelo, M., 2019, PROGRESS IN INDUSTRIAL MATHEMATICS AT ECMI 2018. Faragó, I., Izsák, F. & Simon, P. (eds.). Cham: Springer, p. 313-319 (Mathematics in Industry-Cham; vol. 30).

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

  • Black-Scholes Equation 100%
  • Black-Scholes Model 68%
  • Barrier Options 36%
  • Fractional 35%
  • Model 24%

• Recent Advances in Complex Fluids Modeling

  Rebelo, M., Ferrás, L., Morgado, M. L., Afonso, A. M., McKinley, G. H., Castelo, A. & Leiva, R., 29 May 2019, Fluid Flow Problems. Ali, F. (ed.). InTechOpen , 19 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

  Open Access

  File

  • Fluids 100%
  • Exponential functions 47%
  • Tensors 19%
  • Relaxation 18%
  1 Downloads (Pure)

• Semi-analytical solutions for the Poiseuille–Couette flow of a generalised Phan-Thien–Tanner fluid

  Ribau, Â. M., Ferrás, L. L., Morgado, M. L., Rebelo, M. & Afonso, A. M., 12 Jul 2019, In: FLUIDS. 4, 3, 129.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Flexibility 100%
  • Flow 80%
  • Fluids 80%
  • fluids 73%
  • Purity 63%
  6 Citations (Scopus)

  14 Downloads (Pure)
• 2018

  Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

  Ferrás, L. L., Ford, N. J., Morgado, M. L., Rebelo, M., McKinley, G. H. & Nóbrega, J. M., 30 Sep 2018, In: Computers and Fluids. 174, p. 14-33 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Numerical analysis 100%
  • Sun 78%
  • Fluids 74%
  • Geometry 70%
  • Numerical methods 68%
  17 Citations (Scopus)
• 2017

  Analytical and computational methods for a class of nonlinear singular integral equations

  Allaei, S. S., Diogo, T. & Rebelo, M., Apr 2017, In: Applied Numerical Mathematics. 114, SI, p. 2-17 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Integral equations 100%
  • Analytical Methods 99%
  • Computational methods 98%
  • Singular Integral Equation 96%
  • Computational Methods 96%
  12 Citations (Scopus)

• A primer on experimental and computational rheology with fractional viscoelastic constitutive models

  Ferrás, L. L., Ford, N. J., Morgado, M. L., Rebelo, M., McKinley, G. H. & Nóbrega, J. M., 2017, Novel Trends in Rheology VII. American Institute of Physics, Vol. 1843. 020002

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

  • primers 100%
  • rheology 74%
  • Maxwell fluids 17%
  • calculus 13%
  • Newtonian fluids 13%
  10 Citations (Scopus)

• How non-integer order derivatives can be useful to rheology

  Ferras, L. L., Ford, N. J., Morgado, M. L., Rebelo, M., McKinley, G. H. & Nobrega, J. M., 1 Jan 2017, p. 406-421. 16 p.

  Research output: Contribution to conference › Paper › peer-review

  • Rheology 100%
  • Complex Fluids 54%
  • Graded Meshes 50%
  • Derivative 44%
  • Grading 40%

• Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method

  Morgado, M. L., Rebelo, M., Ferrás, L. L. & Ford, N. J., Apr 2017, In: Applied Numerical Mathematics. 114, p. 108-123 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Chebyshev's Method 100%
  • Collocation 79%
  • Collocation Method 78%
  • Diffusion equation 75%
  • Error analysis 74%
  40 Citations (Scopus)

• Preface: Special Issue: The Fifth International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP 2015), October 22-24, 2015, Lagos, Algarve, Portugal

  Diogo, T., Ford, N., Jackiewicz, Z., Lima, P., Morgado, L. & Rebelo, M., Apr 2017, In: Applied Numerical Mathematics. 114, SI, p. 1-1

  Research output: Contribution to journal › Editorial › peer-review

• Well-posedness and numerical approximation of tempered fractional terminal value problems

  Morgado, M. L. & Rebelo, M., Oct 2017, In: Fractional Calculus and Applied Analysis. 20, 5, p. 1239-1262 24 p.

  Research output: Contribution to journal › Review article › peer-review

  Open Access

  • Numerical Approximation 100%
  • Numerical methods 91%
  • Well-posedness 91%
  • Fractional 74%
  • Shooting Method 63%
  20 Citations (Scopus)
• 2016

  Chebyshev spectral approximation for diffusion equations with distributed order in time

  Morgado, M. L. & Rebelo, M., 2016, Differential and Difference Equations with Applications - ICDDEA, Selected Contributions. Springer New York LLC, Vol. 164. p. 255-263 9 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  • Chebyshev Approximation 100%
  • Spectral Approximation 98%
  • Diffusion equation 73%
  • Forward Problem 51%
  • Expand 40%

• Introducing graded meshes in the numerical approximation of distributed-order diffusion equations

  Morgado, M. L. & Rebelo, M., 20 Oct 2016, Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". American Institute of Physics, Vol. 1776. 070002

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

  • mesh 100%
  • approximation 56%
  • boundary value problems 27%
  • differential equations 21%
  3 Citations (Scopus)

• The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel

  Allaei, S. S., Diogo, T. & Rebelo, M., 1 Nov 2016, In: Siam Journal On Scientific Computing. 69, 2, p. 673-695 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Nonlinear Volterra Integral Equation 100%
  • Jacobi Method 99%
  • Weakly Singular Kernel 98%
  • Integral equations 79%
  • Collocation Method 72%
  14 Citations (Scopus)
• 2015

  An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

  Ford, N. J., Luisa Morgado, M. & Rebelo, M., 2015, In: Electronic transactions on numerical analysis. 44, p. 289-305 17 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Unconditional Stability 100%
  • Finite Difference Approximation 90%
  • Implicit Method 87%
  • Stability and Convergence 81%
  • Diffusion equation 74%
  36 Citations (Scopus)

  245 Downloads (Pure)

• A nonpolynomial collocation method for fractional terminal value problems

  Ford, N. J., Luisa Morgado, M. & Rebelo, M., Feb 2015, In: Journal of Computational and Applied Mathematics. 275, p. 392-402 11 p.

  Research output: Contribution to journal › Article › peer-review

  • Integral equations 95%
  • Differential equations 80%
  23 Citations (Scopus)

• Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

  Rebelo, M., Ferrás, L. & Morgado, M. L., Jul 2015, p. 850-858.

  Research output: Contribution to conference › Paper › peer-review

  • Numerical methods 100%
  • Ordinary differential equations 40%
  • Differential equations 33%
  • Polynomials 29%

• Effect of granular characteristics on the viscoelastic and mechanical properties of native chestnut starch (Castanea sativa Mill)

  Lemos, A. M., Abraao, A. S., Cruz, B. R., Luisa Morgado, M., Rebelo, M. & Nunes, F. M., Oct 2015, In: Food Hydrocolloids. 51, p. 305-317 13 p.

  Research output: Contribution to journal › Article › peer-review

  • Castanea sativa 100%
  • Starch 94%
  • Castanea 86%
  • Gels 79%
  • mechanical properties 55%
  15 Citations (Scopus)

• Fractional Pennes' Bioheat Equation: Theoretical and Numerical Studies

  Ferras, L. L., Ford, N. J., Morgado, M. L., Nóbrega, J. M. & Rebelo, M. S., Aug 2015, In: Fractional Calculus and Applied Analysis. 18, 4, p. 1080-1106 27 p.

  Research output: Contribution to journal › Article › peer-review

  • Derivatives 100%
  • Numerical methods 53%
  • Tissue 51%
  • Mathematical models 41%
  • Hot Temperature 29%
  36 Citations (Scopus)

• Numerical approximation of distributed order reaction-diffusion equations

  Morgado, M. L. & Rebelo, M., Feb 2015, In: Journal of Computational and Applied Mathematics. 275, p. 216-227 12 p.

  Research output: Contribution to journal › Article › peer-review

  • Nonlinear Source 100%
  • Implicit Scheme 86%
  • Source Terms 81%
  • Order of Convergence 81%
  • Reaction-diffusion Equations 77%
• 2014

  A meshfree numerical method for the time-fractional diffusion equation

  Martins, N. F. M. & Rebelo, M. S. D. J., 1 Jan 2014, Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE. p. 892-903

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

• A numerical method for the distributed order time-fractional diffusion equation

  Rebelo, M. S. D. J., 1 Jan 2014, Fractional Differentiation and Its Applications (ICFDA), 2014 International Conference on, IEEE Publisher. p. 1-6

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access
  19 Citations (Scopus)

• A numerical method for the solution of the time-fractional diffusion equation

  Rebelo, M. S. D. J., 1 Jan 2014, Lecture Notes in Computer Science. Murgante, B., Misra, S., Rocha, A. M. A. C., Torre, C., Rocha, J. G., Falcão, M. I., Taniar, D., Apduhan, B. O. & Gervasi, O. (eds.). Switzerland: Springer International Publishing, p. 117-131

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access
  9 Citations (Scopus)

• Fractional modelling of Pennes' bioheat equation using distributed order differential equations

  Rebelo, M. S. D. J., 1 Jan 2014, Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE. p. 507-518

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

• Meshfree methods for nonhomogeneous Brinkman flows

  Martins, N. F. M. & Rebelo, M. S. D. J., 1 Jan 2014, In: Computers and Mathematics with Applications. 68, 8, p. 872-886

  Research output: Contribution to journal › Article › peer-review

  Open Access

• Modelling a competitive antibody/antigen chemical reaction that occurs in the fluorescence capillary-fill device

  Rebelo, M. S. D. J., 1 Jan 2014, Progress in Industrial Mathematics at ECMI 2012. Magnus, F., Michael, G. & Nicole, M. (eds.). Switzerland: Springer, p. 229-236 (Mathematics in Industry; no. 19).

  Research output: Chapter in Book/Report/Conference proceeding › Chapter

• Numerical solution of the reaction-wave-diffusion equation with distributed order in time

  Rebelo, M. S. D. J., 1 Jan 2014, Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering. p. 1057-1068

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
• 2013

  A meshfree method for elasticity problems with interfaces

  Martins, N. F. M. & Rebelo, M. S. D. J., 1 Jan 2013, In: Applied Mathematics and Computation. 219, 22, p. 10732-10745

  Research output: Contribution to journal › Article › peer-review

  Open Access
  11 Citations (Scopus)

• A stokeslets approach for the numerical solution of Brinkman systems

  Martins, N. F. M. & Rebelo, M. S. D. J., 1 Jan 2013, AIP conference proceedings. p. 746-749

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access
  1 Citation (Scopus)

• Fully discretized collocation methods for nonlinear singular Volterra integral equations

  Rebelo, M. S. D. J., 1 Jan 2013, In: Journal of Computational and Applied Mathematics. 247, NA, p. 84-101

  Research output: Contribution to journal › Article › peer-review

  Open Access
  13 Citations (Scopus)

• High order numerical methods for fractional terminal value problems

  Rebelo, M. S. D. J., 1 Jan 2013, In: Computational Methods In Applied Mathematics. 14, 1, p. 55-70

  Research output: Contribution to journal › Article › peer-review

  Open Access
  23 Citations (Scopus)

• Nonpolynomial approximation of solutions to delay fractional di erential equations

  Rebelo, M. S. D. J., 1 Jan 2013, Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, vol. 2, CMMSE 2013, Almeria, Spain, 24­-27 June, 2013, Ian Hamilton & Jesús Vigo-Aguiar (Eds.), 2013. p. 666-676

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

• Nonpolynomial collocation approximation of solutions to fractional differential equations

  Rebelo, M. S. D. J., 1 Jan 2013, In: Fractional Calculus and Applied Analysis. 16, 4, p. 874-891

  Research output: Contribution to journal › Article › peer-review

  Open Access
  60 Citations (Scopus)
• 2012

  A Mathematical Treatment of the Fluorescence Capillary-Fill Device

  Rebelo, M. S. D. J., 1 Jan 2012, In: Siam Journal On Applied Mathematics. 72, 4, p. 1081-1112

  Research output: Contribution to journal › Article › peer-review

  Open Access
  1 Citation (Scopus)

• A non-polynomial collocation method for fractional terminal value problems

  Rebelo, M. S. D. J., 1 Jan 2012, AIP Conference Proceedings. p. 254-257

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

• Numerical methods for nonlinear singular Volterra integral equations

  Rebelo, M. S. D. J., 1 Jan 2012, AIP Conference Proceedings. p. 226-229

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access
  1 Citation (Scopus)

• The method of fundamental solutions for elasticity problems with interfaces

  Martins, N. F. M. & Rebelo, M. S. D. J., 1 Jan 2012, Proceedings of the 7th International Conference Croatian Society of Mechanics (7ICCSM2012). p. 9P - CDROM

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
• 2010

  A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel

  Rebelo, M. S. D. J., 1 Jan 2010, In: Journal of Computational and Applied Mathematics. 234, 9, p. 2859-2869

  Research output: Contribution to journal › Article › peer-review

  Open Access
  28 Citations (Scopus)

• Extrapolation Methods for a Nonlinear Weakly Singular Volterra Integral Equation

  Rebelo, M. S. D. J., 1 Jan 2010, AIP Conference Proceedings. Simos, T., Psihoyios, G. & Tsitouras, C. (eds.). 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA: AMER INST PHYSICS, Vol. 1281. p. 1175-1178

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  1 Citation (Scopus)