Combined Runge-Kutta and Piecewise Constant Argument Methods for Nonlinear Systems of Differential Equations

The applications of the piecewise constant argument method combined with the method are developed for solving first-order nonlinear systems of ordinary differential equations. Using the coefficients of a seventh-order method, a differential equation with piecewise constant arguments is constructed, corresponding to the considered initial value problem and depending on a positive integer N. It is proved that this equation has a unique piecewise-smooth solution, which serves as an approximate solution to the initial value problem for large N. The efficiency of the proposed method is demonstrated through several numerical examples, showing higher accuracy and faster convergence compared to the higher-order Haar wavelet collocation method and other methods reported in the literature.

Keywords

linear ordinary differential equation; piecewise constant argument; approximate solution; method; absolute error.

References

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