Numerical solution for Painlevĕ Equations ii by using integral iteratiye method / Muhammad Hasfizul Rozali and Ahmad Idzham Zulkiflee

Painlevĕ Equations I, II, III, IV, V and VI are solution of nonlinear second-order ordinary differential equations. However, in solving nonlinear problem by using iteration method as one of the solution, the convergence is difficuIt to achieve. Moreover, the previous method such as Adomian Decomposition Method (ADM), Homotophy Perturbation Method (HPM), Variational Iteration Method (VIM) and Sinc-Collocation with Padĕ used to solve the Painlevĕ Equation also quite difficult and the calculation takes large memory in computer. By focusing on solving Painlevĕ Equation II, Integral Iterative Method (IIM) was used to prove in the solving nonlinear differential equation based on the accuracy, efficiency and reliability.Absolute error was used to determine the accuracy and efficiency of Integral Iterative Method (IIM) by computing difference value of Runge-Kutta Method (RK4) and Integral Iterative Method (IIM). Then the value of error will be compared with error of RK4 with other methods such as Daftardar-Gejji and Jafari Method(DJM), Optimai Homotophy Asymptotic Method (OHAM) and Sinc-Collocation.llM is additionally a handy technique in contrast with DJM, OHAM and Sinc-Collocation. The end result is comparable in the direction of DJM. However, IIM are easier to implement as a substitute than DJM. It also show as a dependable approach in fixing Painlevĕ Equation II.