A fourth-order Runge–Kutta method based on BDF-type Chebyshev approximations
نویسندگان
چکیده
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. Themethod thus obtained have good properties relatives to stability including an unbounded stability domain and large -value concerning 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. © 2006 Elsevier B.V. All rights reserved. MSC: 65L05; 65L06; 65L20
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