
Y. A. Burtsev Solving of Cauchy Problem with High Precision Methods Based on Matrix Exponent 

Abstract.
A set of new numerical methods for solving linear ordinary differential equation systems (Cauchy problem) is developed. The methods are based on decomposition of Pade approximation of the matrix exponent to simplest fractions. Homogenous systems can be solved, and nonhomogeneous systems with piecewisepolynomial righthand side function. The new methods are equivalent to some wellknown RungeKutta type methods like Radau and Lobatto methods in terms of accuracy and steady areas. However, new methods are much more simple in theory and practical implementation, and they require several times less computational work. Methods with diagonal Pade approximations are Astable, and methods with subdiagonal Pade approximations are Lstable. New methods can be used for solving stiff, oscillative and stiffoscillative systems.
Keywords:
numerical methods, ordinary differential equations, Cauchy problem, Pade approximation, simplest fractions. PP. 312. DOI: 10.14357/20790279240101
EDN: KPQYBO References
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