in this paper, non-polynomial spline method for solving coupled burgers’ equations are presented. we take a new spline function. the stability analysis using von-neumann technique shows the scheme is unconditionally stable. to test accuracy the error norms2l, ∞l are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equatio...

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has ...

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian struct...

In this work, the G G        -expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the G G        -expansion method provides not only more general forms of solutions but als...

We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries without any recursion operator. The Painlevé analysis easily detects that this is a typical C-integrable system in the Calogero sense and rediscov...

the aim of this paper is to show how some measures of noncompactness in the banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . the results obtained generalize and extend several equations . an illustrative example is also presented .

Global well-posedness, existence of globally absorbing sets and existence of inertial manifolds is investigated for a class of diffusive Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, the Burgers-Sivashinsky equation and the QuasiStedy equation of cellular flames. The global dissipativity is proven in 2D for periodic boundary conditions. For the proof ...