Amiraliyev, G. M.Duru, HakkiAmiraliyeva, I. G.2025-05-102025-05-1020071017-13981572-926510.1007/s11075-007-9096-02-s2.0-34250804428https://doi.org/10.1007/s11075-007-9096-0https://hdl.handle.net/20.500.14720/6795The present study is concerned with the numerical solution, using finite difference method of a one-dimensional initial-boundary value problem for a linear Sobolev or pseudo-parabolic equation with initial jump. In order to obtain an efficient method, to provide good approximations with independence of the perturbation parameter, we have developed a numerical method which combines a finite difference spatial discretization on uniform mesh and the implicit rule on Shishkin mesh(S-mesh) for the time variable. The fully discrete scheme is shown to be convergent of order two in space and of order one expect for a logarithmic factor in time, uniformly in the singular perturbation parameter. Some numerical results confirming the expected behavior of the method are shown.eninfo:eu-repo/semantics/closedAccessUniform ConvergenceDifference SchemeSobolev ProblemSingular PerturbationS-MeshArticle442Q1Q1185203WOS:000247259300007