An easy-to-use variant of the finite difference method (FDM), the polynomial finite difference method (PFDM), for the numerical solution of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), is presented. Compared to the traditional implementation of the FDM, the PFDM approach has two major advantages: straightforward implementation, and easily adjustable accura...

Abstract In this work, we study the A [ ? ] – stability of additive methods Runge- Kutta kind orders ranging from 2 up to 4 that will be applied for determining some stiff nonlinear system ODEs. Moreover, find function Runge-Kutta method and type order 2,3, 4. Where ( A,B 1 ) is A-stable semi-implicit explicit. Furthermore, term managed by while no treated explicit Runge method. Those are suita...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

We introduce a new class of numerical schemes for the solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs). Our algorithms are of the predictor-corrector type; they are obtained via the decomposition of the solutions of the ODEs into combinations of appropriately chosen exponentials, whereas the classical schemes are based on the approximation of solutions by poly...