A Note on Finite Integration Method for Solving Differential Equations
Abstract
The purpose of this article is to present the finite integration method (FIM) for solving nth order differential equation. This article is a reviewed article based on articles published in 2013-2016. The FIM is established by using numerical integration for solving the differential equations. Many numerical integrations have been studied to apply with the FIM. But in this study, we focus on the ordinary linear approximation or the trapezoid rule as the numerical integration which can be formed to be the lower triangular matrix. The use of FIM starts at considering the integral matrix in order to be applied to solve the nth order differential equation by using the n power of one integral matrix which is the advantage of this method, i.e. using only an (one layer) integral matrix to solve any nth order differential equation. This FIM can be applied to solve the ordinary differential equation and the partial differential equation in both cases of time-dependent and independent. This article presents examples of using FIM for solving the ordinary differential equation, the time-dependent partial differential equation in one variable, and the partial differential equation in two variables. Keywords : numerical method, finite integration method, numerical integration, differential equationReferences
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Hairer, E. (1993). Solving Ordinary Differential Equations, vol. 1 and 2, Berlin-New York: Springer-Verlag.
Lambert, J. D. (1991). Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, New York: John Wiley & Sons.
Li, M., Chen, C. S., Hon, Y. C., & Wen, P. H. (2015). Finite integration method for solving multi-dimensional partial differential equations. Applied Mathematical Modelling, 39, 4979-4994.
Li, M., Tian, Z. L., Hon, Y. C., Chen, C. S., & Wen, P. H. (2016). Improved finite integration method for partial differential equations. Engineering Analysis with Boundary Element, 64, 230-236.
Wen, P. H., Hon, Y. C., Li, M., & Korakianitis, T. (2013). Finite integration method for partial differential equations. Applied Mathematical Modelling, 37, 10092-10106.
Hairer, E. (1993). Solving Ordinary Differential Equations, vol. 1 and 2, Berlin-New York: Springer-Verlag.
Lambert, J. D. (1991). Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, New York: John Wiley & Sons.
Li, M., Chen, C. S., Hon, Y. C., & Wen, P. H. (2015). Finite integration method for solving multi-dimensional partial differential equations. Applied Mathematical Modelling, 39, 4979-4994.
Li, M., Tian, Z. L., Hon, Y. C., Chen, C. S., & Wen, P. H. (2016). Improved finite integration method for partial differential equations. Engineering Analysis with Boundary Element, 64, 230-236.
Wen, P. H., Hon, Y. C., Li, M., & Korakianitis, T. (2013). Finite integration method for partial differential equations. Applied Mathematical Modelling, 37, 10092-10106.
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Published
2018-02-08
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Scientific Article
