Numerical solution of differential – difference equations having an interior layer using nonstandard finite differences - Omkar, R.; Lalu, M.; Phaneendra, K. (Karagandy University of the name of acad. E.A. Buketov, 2023)
This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.
Ішкі қабаты бар дифференциалдық-айырымдық теңдеулерді стандартты емес шекті айырымдарды қолданып сандық шешу
Численное решение дифференциально-разностных уравнений с внутренним слоем с использованием нестандартных конечных разностей
Keywords: Differential-difference equation; Boundary layer; Nonstandard finite difference; Convergence