Numerical treatment for the solution of singularly perturbed pseudo-parabolic problem on an equidistributed grid

• Main Authors: Mohapatra Jugal, Shakti Deepti
• Format: Article
• Language: English
• Published: De Gruyter 2020-02-01
• Series: Nonlinear Engineering
• Subjects: pseudo-parabolic problem; singular perturbation; adaptive grid; boundary layer; uniform convergence
• Online Access: https://doi.org/10.1515/nleng-2020-0006

The initial-boundary value problem for a pseudo-parabolic equation exhibiting initial layer is considered. For solving this problem numerically independence of the perturbation parameter, we propose a difference scheme which consists of the implicit-Euler method for the time derivative and a central difference method for the spatial derivative on uniform mesh. The time domain is discretized with a nonuniform grid generated by equidistributing a positive monitor function. The performance of the numerical scheme is tested which confirms the expected behavior of the method. The existing method is compared with other methods available in the recent literature.