Numerical solution of second order Painlevé differential equation
Hijaz Ahmad, Tufail A. Khan, Shao-Wen Yao
Abstract
In this paper, the second order Painlevé differential equation is solved by variational iteration algorithm-I with an auxiliary parameter (VI-I with AP), how to optimally find the auxiliary parameter and Pade approximates for the numerical solution are explained. The effectiveness and suitability of the proposed method are shown by solving two types of second order Painlevé differential equation and the proposed method is compared with other methods to illustrate the accuracy and efficiency of the method.
Topics & Concepts
Order (exchange)MathematicsDifferential equationMathematical analysisApplied mathematicsBernoulli differential equationExact differential equationFirst-order partial differential equationEconomicsFinanceDifferential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsNumerical methods for differential equations