Abstract
In the present paper, we study Legendre Wavelet Method (LWM)
and apply an algorithm based on this approach to solve systems of nonlinear differential equations. Differential equations of any degree can be
expanded as a series in Legendre polynomials. So depending on the kind
of problem, derivative or integral operational matrices appear, after simplification the nonlinear ordinary system changed to an algebraic system
which includes the coefficients. In this step the suggested algorithm is approximated the system of coefficients by using an iterative method. For
comparison, this equation is solved by Moving Least Squares Method
(MLSM) and properties of LWM and MLSM approaches are expressed.
These two approaches are applied to solve an equation that shows effect
and transferring a kind of virus to a set of statistical society. Numerical
results and figures of applying LWM and MLSM are shown finally.
Jafar Biazar, Fereshteh Goldoust. (2019) An Algorithm for Systems of Nonlinear Ordinary Differential Equations Based on Legendre Wavelets, Punjab University Journal of Mathematics, Volume 51, Issue 6.
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