Modification of Levenberg-Marquardt Algorithm for Solve Two Dimension Partial Differential Equation

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 decompositions of Jacobin matrix (J) and inverse of Jacobin matrix( J^-1), if a matrix rectangular or singular  Secondly, we suggest new calculation of μ_k , that ism_k=|| E (w)||²    look the nonlinear execution equations E(w) = 0 has not empty solution W^* and we refer   to the second norm in all cases ,whereE(w):  is continuously differentiable and E(x) is Lipeschitz  continuous, that is=|| E(w ₂)- E(w ₁)||£ L|| w  ₂- w  ₁|| ,where L  is Lipeschitz  constant.