VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
An MEBDF code for stiff initial value problems
ACM Transactions on Mathematical Software (TOMS)
Runge-Kutta methods: some historical notes
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
SIAM Journal on Scientific Computing
A note on the efficient implementation of implicit methods for ODEs
Journal of Computational and Applied Mathematics
A-BDF: A Generalization of the Backward Differentiation Formulae
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations
SIAM Journal on Scientific Computing
Stiff differential equations solved by Radau methods
Proceedings of the on Numerical methods for differential equations
Two low accuracy methods for stiff systems
Applied Mathematics and Computation
An improved class of generalized Runge--Kutta methods for stiff problems-part I: the scalar case
Applied Mathematics and Computation
Blended implementation of block implicit methods for ODEs
Applied Numerical Mathematics
A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
Hi-index | 0.00 |
In this paper, we present error corrected Euler methods for solving stiff initial value problems, which not only avoid unnecessary iteration process that may be required in most implicit methods but also have such a good stability as all implicit methods possess. The proposed methods use a Chebyshev collocation technique as well as an asymptotical linear ordinary differential equation of first-order derived from the difference between the exact solution and the Euler's polygon. These methods with or without the Jacobian are analyzed in terms of convergence and stability. In particular, it is proved that the proposed methods have a convergence order up to 4 regardless of the usage of the Jacobian. Numerical tests are given to support the theoretical analysis as evidences.