An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients

A Kernel-based Collocation Method for Elliptic Partial Differential Equations with Random Coefficients

This paper is an extension of previous work where we laid the foundation for the kernel-based collocation solution of stochastic partial differential equations (SPDEs), but dealt only with the simpler problem of right-hand-side Gaussian noises. In the present paper we show that kernel-based collocation methods can be used to approximate the solutions of high-dimensional elliptic partial differe...

An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

Reduced Basis Collocation Methods for Partial Differential Equations with Random Coefficients

The sparse grid stochastic collocation method is a new method for solving partial differential equations with random coefficients. However, when the probability space has high dimensionality, the number of points required for accurate collocation solutions can be large, and it may be costly to construct the solution. We show that this process can be made more efficient by combining collocation ...

An anisotropic sparse grid stochastic collocation method for elliptic partial differential equations with random input data

This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms (input data of the model). The method consists of a Galerkin approximation in the space variables and a collocation, in probability space, on sparse tensor product grids utilizing either Clenshaw-Curtis or Gaussia...