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22 April 2022 Forward Euler method for ordinary differential equations
Xinyu Kang, Siyu Wang, Jichang Zeng, Yuxuan Zhao
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Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121632U (2022) https://doi.org/10.1117/12.2628078
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China
Abstract
It is feasible to calculate exact expressions for a solution for some basic differential equations. The closed-form solutions to the majority of differential equations, however, are impossible to find. Our aim is to build approximations to differential equation solutions, i.e., to find a function (or a discrete approximation to this function) that satisfies specified relationships between multiple derivatives over a certain domain of space and/or time, as well as some boundary conditions. Generally, only rarely can an analytic formula be found for the solution. The derivatives in differential equations are replaced by finite difference approximations in a finite difference approach. The forward Euler method and its implementation are the major topics of this article. This approach can find the numerical solutions of differential equations and make them almost equal to the precise solutions under specific conditions. Through several examples, we demonstrate how to solve ordinary differential equations using the forward Euler's technique.
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Xinyu Kang, Siyu Wang, Jichang Zeng, and Yuxuan Zhao "Forward Euler method for ordinary differential equations", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121632U (22 April 2022); https://doi.org/10.1117/12.2628078
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KEYWORDS
Differential equations
Numerical analysis
MATLAB
Ordinary differential equations
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