Solution of linear partial differential equations by Lie algebraic methods

Solution of linear partial differential equations by Lie algebraic methods

A new algorithm is proposed for obtaining explicit solutions of the Cauchy problem defined by a certain class of partial differential equations (PDE) of parabolic type. The algorithm exploits the algebraic structure of the problem to transform the PDE into an ordinary matrix differential equation, which is then solved by Lie algebraic techniques.

Solving Partial Differential Equations by Lie Algebraic Methods

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...

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

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.