[1] Ahsan, M., Bohner, M., Ullah, A., Khan, A.A. and Ahmad, S. A haar wavelet multiresolution collocation method for singularly perturbed differential equations with integral boundary conditions, Math. Comput. Simul. 204 (2023), 166–180.
[2] Bakhvalov, N.S. Towards optimization of methods for solving boundary value problems in the presence of boundary layers, Zh. Vychisl. Mat. Mat. Fiz. 9, (1969), 841–859.
[3] Beckett, G. and Mackenzie, J.A. Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem, Appl. Numer. Math. 35(2) (2000), 87–109.
[4] Beckett, G. and Mackenzie, J.A. On a uniformly accurate finite difference approximation of a singularly perturbed reaction–diffusion problem using grid equidistribution, J. Comput. Appl. Math. 131(1-2) (2001), 381–405.
[5] Boor, C. Good approximation by splines with variable knots, In: Spline functions and approximation theory: Proceedings of the Symposium Held at the University of Alberta, Edmonton May 29 to June 1, 1972, Springer, (1973) 57–72.
[6] Cakir, M. and Amiraliyev, G.M. A finite difference method for the singularly perturbed problem with nonlocal boundary condition, Appl. Math. Comput. 160(2) (2005), 539–549.
[7] Chadha, N.M. and Kopteva, N. A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction–diffusion problem, IMA J. Numer. Anal. 31(1) (2011), 188–211.
[8] Das, P. and Mehrmann, V. Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters, BIT Numer. Math. 56(1) (2016), 51–76.
[9] Das, P. and Natesan, S. Higher-order parameter uniform convergent schemes for robin type reaction-diffusion problems using adaptively generated grid, Int. J. Comput. Methods, 9(04) (2012), 1250052.
[10] Das, P., Rana, S. and Vigo-Aguiar, J. Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature, Appl. Numer. Math. 148 (2020), 79–97.
[11] Debela, H.G. and Duressa, G.F. Uniformly convergent numerical method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition, Int. J. Numer. Methods Fluids, 92(12) (2020), 1914– 1926.
[12] Dubeau, F., Elmejdani, S. and Ksantini, R. Non-uniform haar wavelets, Appl. Math. Comput. 159(3) (2004), 675–693.
[13] Goswami, J.C. and Chan, A.K. Fundamentals of wavelets: Theory, algorithms, and applications, John Wiley & Sons, 2011.
[14] Gowrisankar, S. and Natesan, S. The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids, Appl. Math. 26(11) (2013), 1053–1060.
[15] Gowrisankar, S. and Natesan, S. Robust numerical scheme for singularly perturbed convection–diffusion parabolic initial–boundary-value problems on equidistributed grids, Comput. Phys. Commun. 185(7) (2014), 2008–2019.
[16] Haar, A. Zur Theorie der Orthogonalen Funktionensysteme. GeorgAugust-Universitat, Gottingen, 1909.
[17] Hirsch, C. Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics, Elsevier, 2007.
[18] Huang, W. and Russell, R.D. Adaptive moving mesh methods, Springer, 2010.
[19] Kopteva, N., Madden, N. and Stynes, M. Grid equidistribution for reaction–diffusion problems in one dimension, Numer. Algorithms, 40(3) (2005), 305–322.
[20] Kopteva, N., and Stynes, M.A robust adaptive method for a quasi-linear one-dimensional convection-diffusion problem, SIAM J. Numer. Anal. 39(4) (2001), 1446–1467.
[21] Kumar, S. and Kumar, M. Parameter-robust numerical method for a system of singularly perturbed initial value problems, Numer. Algorithms, 59(2) (2012), 185–195.
[22] Kumar, S., Kumar, S. and Sumit, A posteriori error estimation for quasilinear singularly perturbed problems with integral boundary condition, Numer. Algorithms, 89(2) (2022), 791–809.
[23] Kumar, S., Sumit and Vigo-Aguiar, J. A parameter-uniform grid equidistribution method for singularly perturbed degenerate parabolic convection–diffusion problems, J. Comput. Appl. Math. 404 (2020), 113273.
[24] Lepik, U. Numerical solution of differential equations using haar wavelets. Math. Comput. Simul. 68(2), (2005) 127–143.
[25] Lepik, Ü. and Hein, H. Haar wavelets with applications, Springer, New York, 2014.
[26] LeVeque, R.J. Finite difference methods for ordinary and partial differential equations: Steady-state and time-dependent problems, SIAM, 2007.
[27] Liu, L.-B., Long, G. and Cen, Z. A robust adaptive grid method for a nonlinear singularly perturbed differential equation with integral boundary condition, Numer. Algorithms, 83(2) (2020), 719–739.
[28] Mackenzie, J.A. Uniform convergence analysis of an upwind finitedifference approximation of a convection-diffusion boundary value problem on an adaptive grid, IMA J. Numer. Anal. 19(2) (1999), 233–249.
[29] Mallat, S. A wavelet tour of signal processing, Elsevier 1999.
[30] Melenk, J.M. Hp-finite element methods for singular perturbations, Springer, 2002.
[31] Miller, J.J.H., O’Riordan, E. and Shishkin, G.I. Fitted numerical methods for singular perturbation problems: Error estimates in the maximum norm for linear problems in one and two dimensions, World Scientific, 2012.
[32] Pandit, S. and Kumar, M. Haar wavelet approach for numerical solution of two parameters singularly perturbed boundary value problems, Appl. Math. Inf. Sci. 8(6) (2014), 2965.
[33] Podila, P.C. and Sundrani, V. A non-uniform haar wavelet method for a singularly perturbed convection–diffusion type problem with integral boundary condition on an exponentially graded mesh. Comput. Appl. Math. 42(5) (2023), 216.
[34] Qiu, Y. and Sloan, D.M. Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid, J. Comput. Appl. Math. 101(1-2) (1999), 1–25.
[35] Roos, H.G., Stynes, M. and Tobiska, L. Numerical methods for singularly perturbed differential equations, Springer, 1996.
[36] Sah, K.K. and Gowrisankar, S. Richardson extrapolation technique on a modified graded mesh for singularly perturbed parabolic convectiondiffusion problems, Iran. J. Numer. Anal. Optim. 14(1) (2024), 219–264.
[37] Shishkin, G.I. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous boundary conditions, USSR Comput. Math. Math. Phys. 28(6) (1988), 32–41.
[38] Wichailukkana, N., Novaprateep, B. and Boonyasiriwat, C. A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional haar wavelets, Sci. Asia, 42 (2016), 346–355.
[39] Woldaregay, M.M. and Duressa, G.F. Exponentially fitted tension spline method for singularly perturbed differential difference equations, Iran. J. Numer. Anal. Optim. 11(2) (2021), 261–282.
[40] Xu, X., Huang, W., Russell, R.D. and Williams, J.F. Convergence of de Boor’s algorithm for the generation of equidistributing meshes, IMA J. Numer. Anal. 31(2) (2011), 580–596.
[41] Yapman, O. and Amiraliyev, G.M. A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation, Int. J. Comput. Math. 97(6) (2019), 1–10.
