In this paper, spline approximations with five collocation points are used for the
numerical simulation of stochastic of differential equations(SDE). First, we have modeled
continuous-valued discrete wiener process, and then numerical asymptotic st
ochastic
stability of spline method is studied when applied to SDEs. The study shows that the
method when applied to linear and nonlinear SDEs are stable and convergent.
Moreover, the scheme is tested on two linear and nonlinear problems to illustrate
the applicability and efficiency of the purposed method. Comparisons of our results with
Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the
our scheme is better than others.
In this paper, an iterative numerical method for obtaining approximate values of
definite single, double and triple integrals will be illustrated. This method depends on
approximating the single integral function by spline polynomial of fifth degre
e, while
Gauss Legendre points as well as spline polynomials are used for finding multiple
integrals.
The study shows that when the method are applied to single integrals is convergent
of order sixth, as well as when applied to triple integrals is convergent of order sixth for
three Gauss Legendre points or greater.
Errors estimates of the proposed method alongside numerical examples are given to
test the convergence and accuracy of the method.
