Open AccessSome Implicit Fourth and Fifth Order Methods with Optimum Processes for Numerical Initial Value Problems
Author(s) -
Masaharu Nakashima
Publication year - 1985
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195179624
Subject(s) - runge–kutta methods , mathematics , numerical methods for ordinary differential equations , explicit and implicit methods , discretization , scalar (mathematics) , ordinary differential equation , l stability , numerical analysis , initial value problem , differential equation , partial differential equation , numerical stability , stability (learning theory) , mathematical analysis , differential algebraic equation , computer science , geometry , machine learning
§ I. Introduction Many areas of engineering and scientific analysis require methods for solving ordinary or partial differential equations. The progress of digital computer has significantly increased our ability to carry out the numerical solution of such equations, numerous papers have been published which deal with both the theory and practice of such solutions. In the present paper, we concern with the numerical method of the following initial value problem of ordinary differential equation: ( y'=f(x,y) (1-1) I X*o) = JV
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