A novel approximation on the solution of systems of ordinary differential equations
Abstract
In this paper, the initial-value problem for the system of first-order
differential equations is considered. To solve this problem, we construct a
fitted difference scheme using the finite difference method, which is based
on integral identities for the quadrature formula with integral term
remainder terms. Next, we prove first-order convergence for the method in
the discrete maximum norm. Although this scheme has the same rate of
convergence, it has more efficiency and accuracy compared to the classical
Euler scheme. Two test problems are solved by using the proposed method and
the classical Euler method, which confirm the theoretical findings. The
numerical results obtained from here show that the proposed method is
reliable, efficient, and accurate.
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