Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A-BDF: A Generalization of the Backward Differentiation Formulae
SIAM Journal on Numerical Analysis
Stiff differential equations solved by Radau methods
Proceedings of the on Numerical methods for differential equations
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Two low accuracy methods for stiff systems
Applied Mathematics and Computation
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
ARK Methods for stiff problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems
Computer Mathematics
On the relations between B2V Ms and Runge-Kutta collocation methods
Journal of Computational and Applied Mathematics
An Error Corrected Euler Method for Solving Stiff Problems Based on Chebyshev Collocation
SIAM Journal on Numerical Analysis
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In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge-Kutta method having stage order four. The method thus obtained have good properties relatives to stability including an unbounded stability domain and large @a-value concerning A(@a)-stability. A strategy for changing the step size, based on a pair of methods in a similar way to the embedding pair in the Runge-Kutta schemes, is presented. The numerical examples reveals that this method is very promising when it is used for solving stiff initial-value problems.