NUMERICAL METHODS FOR SOLVING FIRST- AND SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS USING EULER'S METHODS
Keywords:
Euler's method, ordinary differential equations, numerical methods, integration step, modified Euler's method, iterative calculationAbstract
This article examines the practical aspects of applying Euler’s numerical method and its modifications to solve first- and second-order ordinary differential equations. The author presents algorithms for constructing successive approximations, a method for estimating error via double integration, and rules for reducing higher-order equations to first-order systems. The work is supplemented with detailed step-by-step examples of manual calculation of iterations, demonstrating the convergence of the method and the possibility of using it to obtain approximate values of the desired function in applied problems.
References
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