Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge–Kutta collocation methods

Ramos, Higinio; García‐Rubio, Raquel

doi:10.1080/00207161003631877

Cited by 6 publications

(10 citation statements)

References 33 publications

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“…Also, the rate of convergence of the SDBDFC2 conforms almost exactly with the order of our methods unlike the ATBM7 and GBDF8. Table 3 shows that the SDBDFC2 is comparable with the CBDF 5 in [22]. Numerical results also show that the new method is consistent with order of the method as the step size decreases.…”

Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 62%

“…Also, the linear system of 3 first order ordinary differential equations solved by Akinfenwa [1], Brugnano and Trigiante [3] and Ramos and Garcia-Rubio [22] given by, 12.00 8.14 10.00…”

Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 99%

“…where err h is the maximum absolute error at step length h. Also in the range 0 ≤ x ≤ 1, AbsErr(t f ) in [22] is obtained by the SDBDFC2 in comparison with the CBDF 5 of degree s = 5 in Ramos and Garcia-Rubio [22] and the following results are presented Table 2, it can be seen that the new method even though it is of order p = 5, performs better that the ATBM7 and the GBDF8, both of orders 7 and 8 respectively. Also, the rate of convergence of the SDBDFC2 conforms almost exactly with the order of our methods unlike the ATBM7 and GBDF8.…”

Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 99%

“…The Chebyshev polynomials is utilized to reasonably spread the errors uniformly on the interval of integration because of its great importance to approximation theory. Also, for several methods on collocation methods for stiff problems see [1,22,23,27]. A continuous multistep formula is generated from this procedure and evaluation at some points yields the block methods which helps to make the implementation procedure self starting.…”

mentioning

confidence: 99%

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A Stiffly Stable Second Derivative Block Multistep Formula With Chebyshev Collocation Points for Stiff Problems

Ehigie¹

2014

Int. J. of Pure and Appl. Math.

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Most block methods in the literature which are implemented in predictor-corrector mode, usually suffer some stability setbacks and this may hinder their implementation on some stiff problems.In this paper, we construct a stiffly stable block second derivative backward differentiation formula with Chebyshev collocation points that is self-starting and is capable of solving stiff problems. The method is applied in block form as a simultaneous numerical integrator over non-overlapping subintervals. The method is proven to possess stiffly stable, A 0 stable and A(α) stable properties. Some numerical examples reveal that this class of methods is very promising and are suitable for solving stiff problems.

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Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 62%

“…Also, the linear system of 3 first order ordinary differential equations solved by Akinfenwa [1], Brugnano and Trigiante [3] and Ramos and Garcia-Rubio [22] given by, 12.00 8.14 10.00…”

Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 99%

Section: Problem 52: a Linear Stiff Problemmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A Stiffly Stable Second Derivative Block Multistep Formula With Chebyshev Collocation Points for Stiff Problems

Ehigie¹

2014

Int. J. of Pure and Appl. Math.

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“…It is noted that Vigo-Aguiar and Ramos [44] also constructed a special family of Runge-Kutta collocation algorithms based on Chebyshev-Gauss-Lobatto points, with A-stability and stiffly accurate characteristics. The interested reader may also refer to [34,35] for additional information.…”

Section: Introductionmentioning

confidence: 99%

A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations

Zhongqing¹

2015

JCM

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In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.Mathematics subject classification: 65L05, 65L60, 41A10.

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An Error Corrected Euler Method for Solving Stiff Problems Based on Chebyshev Collocation

Kim¹,

Piao²,

Kim³

2011

SIAM J. Numer. Anal.

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Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge–Kutta collocation methods

Cited by 6 publications

References 33 publications

A Stiffly Stable Second Derivative Block Multistep Formula With Chebyshev Collocation Points for Stiff Problems

A Stiffly Stable Second Derivative Block Multistep Formula With Chebyshev Collocation Points for Stiff Problems

A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations

An Error Corrected Euler Method for Solving Stiff Problems Based on Chebyshev Collocation

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