Numerical solutions of differential equations having cubic nonlinearity using Boole collocation method
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Abstract
The aim of the study is to develop a numerical method for the solution of cubic nonlinear differential equations in which the numerical solution is based on Boole polynomials. That solution is in the form of the truncated series and gives approximate solution for nonlinear equations of cubic type. In this method, firstly, the matrix form of the serial solution is set and the nonlinear differential equation is converted into a matrix equation system. By adding the effect of both the conditions of the problem and the collocation points to this system of equations, we obtain the new system of equations. The coefficients of Boole-based serial solution are obtained from the solution of the resulting system of equations. The theoretical part is reinforced by considering three test problems. Numerical data for Boole solutions of test problems and absolute error functions are given in tables and figures.