We consider the homogenization of parabolic equations with large spatiallydependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We characterize the leading effect in the random fluctuations and show that their spatial moments converge in law to Gaussian random variables. Both results hold...

in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

The solvability of the fractional partial differential equation with integral overdetermination condition for an inverse problem is investigated in this paper. We analyze direct solution by using “energy inequality” method. Using fixed point technique, existence and uniqueness on data are established.

Abstract We study a first-order nonlinear partial differential equation and present necessary sufficient condition for the global existence of its solution in non-smooth environment. Using this result, we prove local theorem to equation. Moreover, two applications result. The first concerns an inverse problem called integrability microeconomic theory second extension Frobenius’ theorem.

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

In this paper, a new method is proposed in order to evaluate the stochastic solution of linear random differential equation. The method is based on the combination of the probabilistic transformation method for a single random variable and the numerical methods (e.g. finite difference, finite element, Runge-Kutta, etc...). The transformation technique evaluates the probability density function ...