Numerical methods based on multipoint Hermite interpolating polynomials for solving the Cauchy problem for stiff systems of ordinary differential equations |
| |
Authors: | A F Latypov Yu V Nikulichev |
| |
Institution: | (1) Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Institutskaya ul. 4/1, Novosibirsk, 630090, Russia |
| |
Abstract: | Families of A-, L-, and L(δ)-stable methods are constructed for solving the Cauchy problem for a system of ordinary differential equations (ODEs). The L(δ)-stability of a method with a parameter δ ∈ (0, 1) is defined. The methods are based on the representation of the right-hand sides of an ODE system at the step h in terms of two-or three-point Hermite interpolating polynomials. Comparative results are reported for some test problems. The multipoint Hermite interpolating polynomials are used to derive formulas for evaluating definite integrals. Error estimates are given. |
| |
Keywords: | systems of first-order ordinary differential equations Cauchy problem stability Hermite polynomial interpolation error estimate |
本文献已被 SpringerLink 等数据库收录! |