Accelerated Non-standard Numerical Methodfor Two-Parameter Singularly Perturbed Parabolic Problems with Robin Boundary Condition

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Abstract This study devised a robust second-order numerical scheme tosolve two-parameter singularly perturbed parabolic problems with Robin boundary condition. On uniform meshes, the problem is discretized using the implicit Euler method in the time directionand the non-standard finite difference method in the space direction. Also, Robin boundary condition is discretized using the concept of the non-standard finite difference method. The first-order ε-uniform convergence is investigated in both time and space. Applying the Richardson extrapolation technique, the accuracy and convergence rate of the present method have improved from first-orderto second-order. Both theoretical findings and numerical results areagreed upon based on computations of two numerical examples.

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