A computational method for the singularly perturbed delay pseudo-parabolic differential equations on adaptive mesh

References

• E. Abreu and A. Duran, Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models. Comput. Math. with Appl. 102 (2021), pp. 15–44.
   Web of Science ®Google Scholar
• T. Aga Bullo, G.A. Degla, and G.F. Duressa, Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data, J. Appl. Math. Comput. Mech. 20(1) (2021), pp. 5–16.
   Web of Science ®Google Scholar
• T. Aga Bullo, G.F. Duressa, and G.A. Degla, Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems, Comput. Methods Differ. Equ. 9(3) (2021), pp. 886–898.
   Web of Science ®Google Scholar
• I. Amirali, Analysis of higher order difference method for a pseudo-parabolic equation with delay, Miskolc Math. Notes. 20(2) (2019), pp. 755–766.
   Web of Science ®Google Scholar
• I. Amirali and G.M. Amiraliyev, Three layer difference method for linear pseudo-parabolic equation with delay. J. Comput. Appl. Math. 401 (2022). https://doi.org/10.1016/j.cam.2021.113786.
   Google Scholar
• G.M. Amiraliyev, E. Cimen, I. Amirali, and M. Cakir, Higher-order finite difference technique for delay pseudo-parabolic equations, J. Comput. Appl. Math. 321 (2017), pp. 1–7.
   Web of Science ®Google Scholar
• G.M. Amiraliyev and Y.D. Mamedov, Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations, Turk. J. Math. 19 (1995), pp. 207–222.
   Google Scholar
• M. Amrein and T.P. Wihler, An adaptive space-time newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations, IMA J. Numer. Anal. 37(4) (2017), pp. 2004–2019.
   Web of Science ®Google Scholar
• A.R. Ansari, S.A. Bakr, and G.I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math. 205 (2007), pp. 552–566.
   Web of Science ®Google Scholar
• E.B.M. Bashier and K.C. Patidar, A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Appl. Math. Comput. 217(9) (2011), pp. 4728–4739.
   Web of Science ®Google Scholar
• I.P. Boglaev, Approximate solution of a nonlinear boundary value problem with a small parameter for the highest-order differential, USSR Comput. Math. Math. Phys. 24(6) (1984), pp. 30–35.
   Web of Science ®Google Scholar
• A. Bykov, A. Panin, and A. Sharlo, Singularly perturbed pseudoparabolic equation, Math. Methods Appl. Sci. 40(6) (2017), pp. 1949–1963. https://doi.org/10.1002/mma.4111.
   Web of Science ®Google Scholar
• A.B. Chinayeh and H. Duru, On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems, Numer. Methods Partial Differ. Equ. 36 (2019), pp. 228–248.
   Web of Science ®Google Scholar
• A.B. Chinayeh and H. Duru, Uniform difference method for singularly perturbed delay Sobolev problems, Quaest. Math. 43 (2020), pp. 1713–1736.
   Web of Science ®Google Scholar
• P. Das, A higher order difference method for singularly perturbed parabolic partial differential equations, J. Differ. Equ. Appl. 24(3) (2017), pp. 452–477.
   Web of Science ®Google Scholar
• H. Duru, Difference schemes for the singularly perturbed Sobolev periodic boundary problem, Appl. Math. Comput. 149 (2004), pp. 187–201.
   Web of Science ®Google Scholar
• S. Elango, A. Tamilselvan, R. Vadivel, N. Gunasekaran, H. Zhu, J. Cao, and X. Li, Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition, Adv. Differ. Equ. 2021(1) (2021), pp. 1–20.
   Web of Science ®Google Scholar
• R.E. Ewing, Numerical solution of Sobolev partial differential equations, SIAM J. Numer. Anal. 12 (1975), pp. 345–363.
   Web of Science ®Google Scholar
• F.W. Gelu and G.F. Duressa, A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem, Abstr. Appl. Anal. 2021 (2021), pp. 1–11.
   Google Scholar
• L. Govindarao and J. Mohapatra, Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter, Eng. Comput. 37(1) (2019), pp. 289–312.
   Google Scholar
• L. Govindarao and J. Mohapatra, A second order numerical method for singularly perturbed delay parabolic partial differential equation, Eng. Comput. 36(2) (2019), pp. 420–444.
   Google Scholar
• L. Govindarao, S.R. Sahu, and J. Mohapatra, Uniformly convergent numerical method for singularly perturbed time delay parabolic problem with two small parameters, Iran. J. Sci. Technol. Trans. A: Sci. 43 (2019), pp. 2373–2383.
   Web of Science ®Google Scholar
• S. Gowrisankar and S. Natesan, ε-uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations, Int. J. Comput. Math. 94(5) (2017), pp. 902–921.
   Web of Science ®Google Scholar
• H. Gu, Characteristic finite element methods for non-linear Sobolev equations, Appl. Math. Comput.102 (1999), pp. 51–62.
   Web of Science ®Google Scholar
• B. Gunes and H. Duru, A second-order difference scheme for the singularly perturbed Sobolev problems with third type boundary conditions on Bakhvalov mesh, J. Differ. Equ. Appl. 28(3) (2022), pp. 385–405.
   Web of Science ®Google Scholar
• K. Khompysh and A.G. Shakir, An inverse source problem for a nonlinear pseudoparabolic equations with p-Laplacian diffusion and damping term, Quaest. Math. (2022), pp. 1–26. https://doi.org/10.2989/16073606.2022.2115951.
   Google Scholar
• D. Kumar and P. Kumari, A parameter-uniform scheme for singularly perturbed partial differential equations with a time lag, Numer. Methods Partial Differ. 36(4) (2020), pp. 868–886.
   Web of Science ®Google Scholar
• S. Kumar and M. Kumar, High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay, Comput. Math. Appl. 68 (2014), pp.1355–1367.
   Web of Science ®Google Scholar
• R. Luce, N. Seam, and G. Vallet, 1D numerical simulation for nonlinear pseudoparabolic problems, Monografias Matematicas Garcia De Galdeano. 37 (2012), pp. 161–170.
   Google Scholar
• N.A. Mbroh, S.C.O. Noutchime, and R.Y.M. Massoukou, A robust method of lines solution for singularly perturbed delay parabolic problem, Alexandria Eng. J. 59 (2020), pp. 2543–2554.
   Web of Science ®Google Scholar
• J. Mohapatra and D. Shakti, Numerical treatment for the solution of singularly perturbed pseudo-parabolic problem on an equidistributed grid, Nonlinear Eng. 9 (2020), pp. 169–174.
   Google Scholar
• N.H. Nhan, T.T.M. Dung, L.T.M. Thanh, L.T.P. Ngoc, and N.T. Long, A high-order iterative scheme for a nonlinear pseudoparabolic equation and numerical results, Math. Probl. Eng. 2021 (2021), pp. 1–17.
   Web of Science ®Google Scholar
• A.A. Samarski, The Theory of Difference Schemes, M.V. Lomonosov State University, Moscow, 2001.
   Google Scholar
• S. Tian, X. Liu, and R. An, A higher-order finite difference scheme for singularly perturbed parabolic problem, Math. Probl. Eng. 2021 (2021), pp. 1–11. https://doi.org/10.1155/2021/9941692.
   Google Scholar
• M.M. Woldaregay, W.T. Aniley, and G.F. Duressa, Novel numerical scheme for singularly perturbed time delay convection-diffusion equation, Adv. Math. Phys. 2021 (2021), pp. 1–13. https://doi.org/10.1155/2021/6641236.
   Web of Science ®Google Scholar
• S. Yadav and P. Rai, A higher order scheme for singularly perturbed delay parabolic turning point problem, Eng. Comput. 38 (2020), pp. 819–851.
   Google Scholar
• C. Zhang and Z. Tan, Linearized compact difference methods combined with Richardson extrapolation for nonlinear delay Sobolev equations. Commun. Nonlinear Sci. Numer. Simul. 91 (2020). 105461.
   Web of Science ®Google Scholar