On Runge-Kutta Formulae with the Ability of Error Estimation : In the Case of the Function with one Variable

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概要

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• In this paper, we study on some Runge-Kutta formulae with the estimating ability of truncation error which are expressed as below. [numerical formula] where the ordinary differential equation is : (dy)/(dx)=f(x), y(x_0)=y_0 and also where α_i, ν_i and μ_i are scalars, y_1 stands for an integral formula, and y_2,a formula with higher accuracy than y_1. T, the difference between y_1 and y_2,gives us the estimated value of the truncation error that y_1 has. In this paper, the cases of m=3,4 and 5 will be studied. While deciding the coefficients, we use the degrees of freedom for the purpose of raising up the accuracy of both y_1,the integral formula and T, the estimated truncation error.

• 山梨大学の論文
• 1967-12-20

著者

• Tanaka Masatsugu

  山梨大学工学部

関連論文

• On Runge-Kutta Formulae with the Ability of Error Estimation : In the Case of the Function with one Variable

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