An explicit two-step rational method for the numerical solution of first order initial value problem

Ying, Teh Yuan

doi:10.1063/1.4887571

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…Such approaches have stronger stability properties as well. Some non-linear or one-step rational schemes in [16,17] or two-step in [18] are applicable for stiff and singular types of non-linear initial value problems. These schemes deal with the singularities at a pole at a given time interval with a low computational cost.…”

Section: Introductionmentioning

confidence: 99%

A new nonlinear L-stable scheme with constant and adaptive step-size strategy

Arain¹,

Qureshi²,

Shaikh³

2021

J. Appl. Math. Comput. Mech.

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The present study proposes a new explicit nonlinear scheme that solves stiff and nonlinear initial value problems in ordinary differential equations. One of the promising features of this scheme is its fourth-order convergence with strong stability having an unbounded region. A modern approach for relative stability growth analysis is also presented under order stars conditions. The scheme is also good in dealing with singular and stiff type of models. Comparing numerical experiments using various errors, including maximum absolute global error over the integration interval, absolute error at the endpoint, average error, norm of errors, and the CPU times (seconds), shows better performance. An adaptive step-size approach seems to increase the performance of the proposed scheme. The numerical simulations assure us of L -stability, consistency, order, and rapid convergence.

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Section: Introductionmentioning

confidence: 99%

A new nonlinear L-stable scheme with constant and adaptive step-size strategy

Arain¹,

Qureshi²,

Shaikh³

2021

J. Appl. Math. Comput. Mech.

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“…In all cases, it was shown that their method possesses better approximation, more efficient and needs shorter execution time than the Taylor method. Ying et al [4] considered…”

Section: Introductionmentioning

confidence: 99%

On nonlinear methods for stiff and singular first order initial value problems

Adesanya¹,

Pantuvo²,

Umar³

2018

nade

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This paper considers development of nonlinear method by interpolation and collocation of inverse polynomial approximate solution to give systems of equations, solving for the unknown parameters and substituting the results into the approximate solution gives a continuous method. We evaluated the continuous method at different grid points to give discrete methods which are implemented without developing separate predictors. The method is convergent and A-stable, numerical examples show that the method is good for stiff and singular problems.

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“…Such problems are found in the modeling of disease outbreak, war, radioactive decay, di¤usion process in biology and chemical reactions. Several scholars have developed exponentially …tted methods are the best methods for (1:1) among them are [1][2][3][4][5][6][7][8] .…”

Section: Introductionmentioning

confidence: 99%

New algorithm for problems with exponential solutions

Adesanya¹,

Onsachi²,

R³

2016

Preprint

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In this paper, we consider the development of algorithms for the solution of first order initial value problems whose solution exhibits exponential behaviour. Method of interpolation and collocation of basis function to give system of nonlinear equations which is solved for the unknown parameters to give a continuous scheme. The discrete methods recovered from the continuous scheme are implemented in block form. The stability properties of the method is verified and numerical experiments show that our method is efficient in handling these problems

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An explicit two-step rational method for the numerical solution of first order initial value problem

Cited by 6 publications

References 11 publications

A new nonlinear L-stable scheme with constant and adaptive step-size strategy

A new nonlinear L-stable scheme with constant and adaptive step-size strategy

On nonlinear methods for stiff and singular first order initial value problems

New algorithm for problems with exponential solutions

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