@techreport{oai:ipsj.ixsq.nii.ac.jp:00145097,
 author = {平山, 弘 and Hiroshi, Hirayama},
 issue = {14},
 month = {Sep},
 note = {Taylor 級数の四則演算および関数は C++ 言語によって容易にできる．四則演算，関数，条件文等で記述された C++ 言語で定義された関数は容易に Taylor 展開できる．解は任意次数まで計算できるので，Runge-Kutta に代わる任意次数の公式として使うことができる．Taylor 級数を使えば，誤差評価も容易に行え，許容誤差内の適切なステップサイズを容易に求められる．さらに，べき級数を Pade 展開に変換し，それを利用すると任意次数で A 安定な常微分方程式を解く数値計算法を与える．偏微分方程式を空間的に差分化し，得られる連立常微分方程式を時間方向にべき級数法を適用して解くことを提案する．この方法を使うと安定で精度の高い計算ができる．本文では，空間方向に精度の高いコンパクト差分近似法を使って，偏微分方程式を連立常微分方程式で高精度で近似し，それを A 安定な Taylor 展開法で解き，精度の高い計算が出来た．例題の拡散方程式では，絶対誤差が 10-10 程度以下の計算が出来た．, The arithmetic operations and functions of Taylor series can be facilitated by the C ++ language. The C++ function written by arithmetic operations, functions, and conditional statements, etc. can be easily Taylor expansion. As we can calculate the solution to any degree, we can be used as the higher order formula to replace the Runge-Kutta. Using the Taylor series, error evaluation also easily be carried out, it can be easily obtained the appropriate step size within tolerance. In addition, it should be to convert the series to Pad 'e series, to give a numerical calculation method to solve the A stable ordinary differential equations in any order when you use it. The partial differential equations spatially differencing, we propose to solve by applying the series method to the simultaneous ordinary differential equations in the time direction which is obtained. This method can be highly stable and accurate calculations when you use it. In this paper, by using the compact differential approximation accurate in the spatial direction, it is approximated with high accuracy to partial differential equations in a system of ordinary differential equations, It can be solved by A stable Taylor expansion method, we can get highly accurate results. In the diffusion equation of example, we can get good results whose the absolute error is less than or almost equal to 10-10.},
 title = {Taylor展開法による偏微分方程式の数値解法},
 year = {2015}
}