KEKONVERGENAN SOLUSI PERSAMAAN DIFERENSIAL BIASA ORDE SATU MENGGUNAKAN METODE ITERASI VARIASIONAL

Abstract

Ordinary differential equation (ODE) is an equation involving derivatives of one or more dependent variables with respect to single independent variable. ODE is grouped into two part; linear and nonlinear. There are some methods to determine the solution of nonlinear ODE, one of them is Variational Iteration Method. This method create a correction functional using general Lagrange multiplier and a restricted variational. The purpose of this research is to prove convergence and solution ordinary differential equation using variational iteration method. This study was conducted by literary method. This result is show that If operator of correction satisfy contraction inequality ‖𝑣𝑣𝑘𝑘+1‖≤𝛾𝛾 ‖𝑣𝑣𝑘𝑘‖ where 0<𝛾𝛾<1, then series solution from differential equation nonlinear converge to exact solution and can be used to determine the nonlinear solution.