Diagonal Padé Approximations for Initial Value Problems
- 1 September 1988
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific and Statistical Computing
- Vol. 9 (5) , 829-838
- https://doi.org/10.1137/0909055
Abstract
Diagonal Padé approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained.Keywords
This publication has 15 references indexed in Scilit:
- Absolute monotonicity of rational functions occurring in the numerical solution of initial value problemsNumerische Mathematik, 1986
- The Lorenz model and the method of Carleman embeddingPhysics Letters A, 1981
- Nineteen Dubious Ways to Compute the Exponential of a MatrixSIAM Review, 1978
- The Solution of Tridiagonal Linear Systems on the CDC STAR 100 ComputerACM Transactions on Mathematical Software, 1975
- Methods of Numerical MathematicsPublished by Springer Nature ,1975
- A-Stable Methods and Padé Approximations to the ExponentialSIAM Journal on Mathematical Analysis, 1973
- Discretization Errors for Well-Set Cauchy Problems. I.Journal of Mathematics and Physics, 1965
- On some questions arising in the approximate solution of nonlinear differential equationsQuarterly of Applied Mathematics, 1963
- A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction typeMathematical Proceedings of the Cambridge Philosophical Society, 1947
- Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéairesActa Mathematica, 1932