A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations

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...

Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.

Chebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

Computational technique of linear partial differential equations by reduced differential transform ‎method

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

A numerical method for solving a class of distributed order time-fractional diffusion partial differential equations according to Caputo-Prabhakar fractional derivative

In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed nu...