Step-By-Step Application of Shifted Legendre Polynomials on Numerical Assessment of Non-Linear Bratu Differential Equations

The approximate solution of Bratu differential equations was obtained using the modified variational iteration algorithm with shifted Legendre polynomials. The suggested modification is created by constructing shifted Legendre polynomials for the provided problem and using them as the basis functions for the approximation. To show that the recommended approach is efficient, dependable, and reliable, two test problems were also provided. The maple 18 program was used to perform the calculations. Keyword: Differential equations, variational iteration technique, shifted Legendre polynomials, bratu equations, approximate solution.