Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator

Ramos, Higinio; Singh, Gurjinder

doi:10.1016/j.amc.2022.126960

Cited by 6 publications

(2 citation statements)

References 40 publications

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“…Several scholars have developed various iterative techniques for numerically integrating different kinds of differential systems. For example, the authors in [43] have developed an efficient third-derivative hybrid block approach for integrating secondorder two-point BVPs with Dirichlet, Neumann, or Robin boundary conditions. A method was developed using interpolation and collocation.…”

Section: Introductionmentioning

confidence: 99%

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

Baleanu,

Qureshi,

Soomro

et al. 2024

J. Math. Computer Sci.

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This paper proposes an optimal time-efficient numerical method for solving the initial value problems (IVPs) of ordinary differential equations (ODEs) that is both A-stable and hyperbolically fitted. The method is designed to handle both constant and variable step sizes, making it highly adaptable to different types of ODEs. The methodology proposed herein leverages the optimization of an off-grid point, derived from the predominant term of the local truncation error, to enhance both accuracy and stability in the solution of stiff ODEs. This approach incorporates a variable step size control, predicated upon the error estimation furnished by the embedded pair, and aims to minimize computational expenses while concurrently safeguarding both precision and stability. Furthermore, the stability domain of the proposed method is demonstrated to be optimal, signifying it encompasses the maximal conceivable set of step sizes wherein the method retains its stability. Other important measures including zero-stability, consistency, and convergence are also discussed theoretically and confirmed experimentally. Numerical experiments consisting of the Duffing system, sinusoidal stiff system, periodic orbit system, two-body system, Lorenz system, and the system for catenary equation demonstrate that the proposed method is highly competitive in terms of accuracy and efficiency, and outperforms several existing methods for solving stiff ODEs with both constant and variable step sizes.

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Section: Introductionmentioning

confidence: 99%

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

Baleanu,

Qureshi,

Soomro

et al. 2024

J. Math. Computer Sci.

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“…Several scholars have developed and used various approximate techniques for numerically integrating the type of problems under consideration. Some of these methods are the finite difference method, collocation method, spectral method, Galerkin method, variational iteration method, the Rayleigh-Ritz method, B-spline technique, the Adomian decomposition method, a fixed-point iteration with Green's functions method, finite-element technique, B-spline linear multistep method, block method, the simple Homotopy perturbation method, higher derivative hybrid block techniques, or the trigonometrically fitted predictor-corrector method (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]).…”

Section: Introduction and Description Of The Problemmentioning

confidence: 99%

An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

Rufai

2022

Mathematics

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A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such as consistency and convergence, are well analysed. Some BVPs with different boundary conditions are solved to demonstrate the efficiency and feasibility of the suggested method. The numerical results of the proposed method are much closer to the exact solutions and more competitive than other numerical methods in the available literature.

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Application of linear Legendre multi-wavelets collocation method for solution of fourth order boundary value problems

Khan,

Ansari,

Amin

et al. 2024

Engineering with Computers

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Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator

Cited by 6 publications

References 40 publications

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

Application of linear Legendre multi-wavelets collocation method for solution of fourth order boundary value problems

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