A random Laplace transform method for solving random mixed parabolic differential problems

Solving Random Differential Equations by Means of Differential Transform Methods

In this paper the random Differential Transform Method (DTM) is used to solve a time-dependent random linear differential equation. The mean square convergence of the random DTM is proven. Approximations to the mean and standard deviation functions of the solution stochastic process are shown in several illustrative examples. AMS Subject Classifications: 65L20, 60G15, 39A10.

An application of differential transform method for solving nonlinear optimal control problems

In this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (OCP's). The approach rest mainly on the differential transform method (DTM) which is one of the approximate methods. The DTM is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. Utilizing this approach, the optimal co...

A High Order Finite Dierence Method for Random Parabolic Partial Dierential Equations

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...

On the Laplace transform decomposition algorithm for solving nonlinear differential equations

A numerical scheme for solving nonlinear backward parabolic problems

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...