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In this paper, the authors using the MATLAB software to the ordinary differential equation initial value problem, Euler's method, improved Euler method, classical Runge-Kutta method is used for computer programming and implementation, through the comparison of numerical results analysis, Euler method principle simple error is bigger, improved Euler method to calculate the amount is larger, the classical Runge-Kutta method for high precision stability is also very good.

Comparison of Several Numerical Algorithms for Solving Ordinary Differential Equation Initial Value Problem