[1] Amiraliyev, G.M. and Amiraliyeva, I.G. Difference schemes for the sin-gularly perturbed Sobolev equations, In Difference Equations, Special Functions And Orthogonal Polynomials, 2007, 23–40.
[2] Amiraliyev, G.M., Duru, H. and Amiraliyeva, I.G. A parameter-uniform numerical method for a Sobolev problem with initial layer, Numer. Al-gorithms 44 (2007), 185–203.
[3] Amiraliyev, G.M. and Mamedov, Y.D. Difference schemes on the uni-form mesh for singularly perturbed pseudo-parabolic equations, Turk. J. Math. 19 (3) (1995), 207–222.
[4] Barenblatt, G.I., Zheltov, I.P. and Kochina, I.N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], J. Appl. Math. Mech. 24 (5) (1960), 1286–1303.
[5] Chen, P.J. and Gurtin, M.E. On a theory of heat conduction involving two temperatures, J. Appl. Math. Phys. 19 (1968), 614–627.
[6] Ciftci, I. and Halilov, H. Dependency of the solution of quasilinear pseu-doparabolic equation with periodic boundary condition on ε, Int. J. Math. Anal. 2 (2008), 881–888.
[7] Duressa, G.F. and Reddy, Y.N. Domain decomposition method for sin-gularly perturbed differential difference equations with layer behavior, Int. J. Eng. Sci. 7 (1) (2015), 86–102.
[8] Duru, H. Difference schemes for the singularly perturbed Sobolev periodic boundary problem, Appl. Math. Comput. 149 (1) (2004), 187–201.
[9] Geng, F., Tang, Z. and Zhou, Y. Reproducing kernel method for sin-gularly perturbed one-dimensional initial-boundary value problems with exponential initial layers, Qual.Theory Dyn. Syst. 17 (1) (2018), 177–187.
[10] Gunes, B. and Duru, H. A second-order difference scheme for the singu-larly perturbed Sobolev problems with third type boundary conditions on Bakhvalov mesh, J. Differ. Equ. 28 (3) (2004), 385–405.
[11] Huilgol, R.R. A second order fluid of the differential type, Int. J. Non-Linear Mech. 3 (4) (1968), 471–482.
[12] Jiwari, R. Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model, Math. Comput. Simul. 198 (2022), 106–126.
[13] Jiwrai, R. and Mittal, R.C. A higher order numerical scheme for singu-larly perturbed Burger-Huxley equation, J. Appl. Math. Inform. 29 (3-4) (2011), 813–829.
[14] Jiwari, R., Singh, S. and Singh, P. Local RBF-FD-based mesh-free scheme for singularly perturbed convection-diffusion-reaction models with variable coefficients, J. Math. 2022 (2022), 1–11.
[15] Kadalbajoo, M.K. and Patidar, K.C. Singularly perturbed problems in partial differential equations: A survey, Appl. Math. Comput 134 (2-3) (2003), 371–429.
[16] Kumar, N., Toprakseven, Ş. and Jiwari, R. A numerical method for sin-gularly perturbed convection–diffusion–reaction equations on polygonal meshes, Comput. Appl. Math. 43 (1) (2024), 44.
[17] Mohapatra, J. and Shakti, D. Numerical treatment for the solution of singularly perturbed pseudo-parabolic problem on an equidistributed grid, Nonlinear Eng. 9 (1) (2020), 169–174.
[18] Nikolis, A. and Seimenis, I. Solving dynamical systems with cubic trigonometric splines, Appl. Math. [E-Notes] 5 (2005), 116–123.
[19] Schoenberg, I.J. On trigonometric spline interpolation, J. math. mech. (1964), 795–825.
[20] Van Duijn, C.J., Fan, Y., Peletier, L.A. and Pop, I.S. Traveling wave solutions for degenerate pseudo-parabolic equations modeling two-phase flow in porous media, Nonlinear Anal.: Real World Appl. 14 (3) (2013), 1361–1383.
[21] Vijayakumar, V., Udhayakumar, R. and Kavitha, K. On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay, Evol. Equ. Control Theory. 10 (2) (2021), 271–296.
[22] Zahra, W.K. Trigonometric B-spline collocation method for solving PHI-four and Allen–Cahn equations, Mediterr. J. Math. 14 (2017), 1–19.
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