Collocation Method with Shifted Legendre-Based Approach for Solution of Nonlinear Differential Equations
DOI:
https://doi.org/10.26713/cma.v17i1.3564Keywords:
Shifted Legendre Polynomial, Collocation method, L2-Norm, Nonlinear Ordinary Differential Equations, Numerical ApproximationAbstract
The technique of solving nonlinear ordinary differential equation (NODE) that we have
used in the paper is the Shifted Legendre technique. This is achieved by rewriting the
problem in a more stable way with Shifted Legendre polynomials which has been shown to
be effective and precise in numerical solutions. Using this method allows solving complicated
nonlinear equations and it is not difficult to obtain approximate solutions in a short time. The
paper identifies the benefits of the given approach, that is, reduced computing requirements
and enhanced precision and is supported by practical exercises. The up-to-date analysis of
the solution of nonlinear ordinary differential equations (NODEs) by the Shifted Legendre
technique provides a simple and easily applicable answer. Numerical findings of the applied
method demonstrate the exact correspondence with the exact solution with the least errors
that is better in comparison with the current methods. A number of examples are resolved
to demonstrate the success of the suggested method with minimum errors that outperform
the existing methods.
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