Since,

partial differential equations in the coupled problem under consideration had complicated mixed partial derivatives (Handibag and Karande, 2012).

We calculated the Ricci tensors of the spacetimes given in equation (4) and put them equal to zero we get the following system of four non-linear

partial differential equations in unknown functions (eqs.

and then setting each coefficient to zero, we can get a set of overdetermined

partial differential equations for [a.

According to [8], and [9], in the last four decades the range of application of Lie theory deals among others with the following topics: algorithmic determination of differential system symmetry groups, determination of explicit solutions for nonlinear

partial differential equations, conservation laws, classification of integrable systems, numeric methods and solution stability [5].

A linear

partial differential operator in 2n +1 independent variables z,[x.

The MOL method algebraically approximates boundary value partial derivatives, and so reduces

partial differential equations to ordinary differential equations.

The approach avoids the breakdowns that plague models based on

partial differential equations, Griffeath says.

The new mesh generation routines will be of particular relevance to those working with multi-dimensional

partial differential equations, particularly using Finite Element or Finite Volume methods.

The group with the

partial differential condition consisted of 4 males and 17 females and had a mean age of 22.

Finite difference methods for

partial differential equations

is a flexible system that solves

partial differential equation problems, thus eliminating the need to buy and learn a new software tool for each problem.

With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear

partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems.