METODE DEKOMPOSISI LAPLACE UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL PARSIAL NONLINIER

Abstract

Partial differential equations are grouped into two parts: linear and nonlinear differential equations. Many natural phenomena are modeled in the form of nonlinear partial differential equations, such as K-dV and Burger equations. To be able to explain natural phenomena in the form of nonlinear partial differential equations required approach method which can then be applied to determine the solution of partial differential equation. One of the methods used to determine the solution of nonlinear differential equations is Laplace Decomposition Method which combines Laplace Transformation theory and Adomian Decomposition Method. This research is conducted by using literature method with the following procedure: Assessing Non-Linear Partial Differential Equation, Method Adomian Decomposition, Laplace Transformation and Laplace Decomposition Method; then determine the settlement of the non-linear differential equation with the Laplace Decomposition Method. The result of this research is obtained by solution of nonlinear partial differential equation of Order one by using Laplace decomposition method that is 0nnuu∞ == Σ with (𝑥𝑥, 𝑡𝑡) = ℒ-1􁉂1𝑠𝑠ℒ {𝑔𝑔 (𝑥𝑥, 𝑡𝑡)} + 1𝑠𝑠ℎ (𝑥𝑥) 􁉃 and 𝑢𝑢𝑛𝑛 + 1 (𝑥𝑥, 𝑡𝑡) = ℒ-1􁉂-1𝑠𝑠ℒ {𝑅𝑅𝑅 𝑛𝑛 (𝑥𝑥, 𝑡𝑡) } -1𝑠𝑠ℒ {𝐴𝐴𝑛𝑛} 􁉃; 𝑛𝑛≥0 and on the two-order nonlinear partial differential equation is 0nnuu = = Σ with 𝑢𝑢0 (𝑥𝑥, 𝑡𝑡) = ℒ-1􁉂1𝑠𝑠2ℒ {𝑔𝑔 (𝑥𝑥, 𝑡𝑡)} + 1𝑠𝑠ℎ (𝑥𝑥) + 1𝑠𝑠2𝑘𝑘 (𝑥𝑥) 􁉃 and 𝑢𝑢𝑛𝑛 + 1 (𝑥𝑥, 𝑡𝑡) = ℒ-1􁉂-1𝑠𝑠2ℒ {𝑅𝑅𝑅 𝑛𝑛 (𝑥𝑥, 𝑡𝑡)} - 1𝑠𝑠2ℒ {𝐴𝐴𝑛𝑛} 􁉃; 𝑛𝑛≥0