SOLUSI PERSAMAAN DIFERENSIAL PARSIAL LINIER ORDE DUA MENGGUNAKAN METODE POLINOMIAL TAYLOR

Abstract

Partial differential equation is an equation containing a partial derivative of one or more dependent variables on more than one independent variable. In the differential equation there are coefficients in the form of constants and functions. The solution of a partial differential equation whose coefficients are constants is easily determined. However, the solution of the differential equations whose coefficients are functions is quite difficult to determine. One method that can be used to determine the solution is by using Taylor polynomial. This method can be used in second-order linear partial differential equation with coefficient of function with two independent variables. The purpose of this research is to determine the Taylor polynomial solution on second-order linear partial differential equation. In this research we get solution from second-order linear partial differential equation by assuming solution in the form of polynomial of Taylor having degree 𝑁𝑁 𝑢𝑢 (𝑥𝑥, 𝑦𝑦) = 􀷍􀷍αα𝑟𝑟, 𝑠𝑠 (𝑥𝑥-𝑐𝑐0) 𝑟𝑟 (𝑦𝑦-𝑐𝑐1) 𝑠𝑠, 𝑁𝑁𝑠𝑠 = 0𝑁𝑁𝑟𝑟 = 0 with αα𝑟𝑟, 𝑠𝑠 = 1𝑟𝑟! 𝑠𝑠! 𝑢𝑢 (𝑟𝑟, 𝑠𝑠) (𝑐𝑐0, 𝑐𝑐1) is the Taylor polynomial coefficient, or can be expressed in terms of the matrix equation 𝑢𝑢 (𝑥𝑥, 𝑦𝑦) = 𝑋𝑋𝑋𝑋𝑋𝑋