Modification Of Levenberg-Marquardt Algorithm For Solve Two Dimension Partial DifferentialEquation

Abstract

In this paper we presented a new way based on neural network has been developed for solutione of two dimension partial differential equations . A modified neural network use to over passing the Disadvantages of LM algorithm, in the beginning we suggest signaler value decompositionsof Jacobin matrix (J) and inverse of Jacobin matrix( J-1), if J(w) is a matrix rectangular or singular. Secondly, we suggest new calculation of μk , that isk= E (w)2.look the nonlinear execution equationsE(w) = 0 has not empty solutionW* and we refer ‖∙‖ to the second norm in all cases ,whereE(w): R^n→R^m is continuously differentiable and E(x) is Lipeschitz continuous, that is= E(w2)- E(w1) L w2- w1,where L is Lipeschitz constant.