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2006•Chinese PhysicsRequires access

Hamilton–Jacobi method for solving ordinary differential equations

Mei Feng-Xiang, Huibin Wu, Zhang Yong-Fa

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Abstract

The Hamilton–Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton–Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.

About this research paper

What this paper is about

The Hamilton–Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton–Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The Hamilton–Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton–Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.

Key concepts: Hamilton–Jacobi equation, Ordinary differential equation, Integrating factor, Collocation method, Mathematics, Examples of differential equations, Separable partial differential equation, Differential equation

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