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 right-hand side function. The new methods are equivalent to some well-known Runge-Kutta 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 A-stable, and methods with subdiagonal Pade approximations are Lstable. New methods can be used for solving stiff, oscillative and stiff-oscillative systems.

Keywords: 

numerical methods, ordinary differential equations, Cauchy problem, Pade approximation, simplest fractions.

 

PP. 3-12.

 

 

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