In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

The main purpose of this paper is to solve an inverse random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the inverse problem by solving the inverse random differential equation using Crank-Nicholson's method. Then, using the particle swarm optimization algorith...

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

It is known that if a stochastic process is a solution to a classical Itô stochastic differential equation (SDE), then its transition probabilities satisfy in the weak sense the associated Cauchy problem for the forward Kolmogorov equation. The forward Kolmogorov equation is a parabolic partial differential equation with coefficients determined by the corresponding SDE. Stochastic processes whi...

Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opin...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...