Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Uwaheren, O. A.; Adebisi, A. F.; Ishola, C Y; Raji, M. T.; Yekeem, A. O.; Peter, Olumuyiwa James

doi:10.30598/barekengvol16iss3pp1123-1130

Cited by 3 publications

(1 citation statement)

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“…The suggested method involved the application of the homotopy perturbation method and the initial approximation as the constructed orthogonal polynomials. [21] presented Akbari-Ganji's Method (AGM) to solve Volterra Integro-Differential Difference Equations (VIDDE) using Legendre polynomials as basis functions. A trial solution function of unknown constants that conform with the differential equations together with the initial conditions were assumed and substituted into the equations under consideration.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method using Collocation Approach for the Solution of Volterra-Fredholm Integro-Differential Equations

Ajileye

Aminu

2022

Afr. Sci. Rep.

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This paper consider collocation approach for the numerical solution of Volterra-Fredholm Integro-differential equation using collocation method. We transformed the problem into a system of linear algebraic equations and matrix inversion is adopted to solve the algebraic equations. We substituted the solution algebraic equations into the approximate equation to obtain the numerical result. Some numerical problems are solved to demonstrate the efficiency and consistency of the method.

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Section: Introductionmentioning

confidence: 99%

A Numerical Method using Collocation Approach for the Solution of Volterra-Fredholm Integro-Differential Equations

Ajileye

Aminu

2022

Afr. Sci. Rep.

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Numerical simulation of Volterra PIDE with singular kernel via modified cubic exponential and uniform algebraic trigonometric tension B-spline DQM

Kaur,

Kapoor

2024

Mathematics and Computers in Simulation

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On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations

Shams

2024

Mathematics

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Fractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predictions regarding outcomes across a range of applications where these problems are effectively addressed. This research introduces a novel hybrid multiplicative calculus-based parallel method for solving complex nonlinear models in engineering. To speed up the method’s rate of convergence, we utilize a second-order multiplicative root-finding approach as a corrector in the parallel framework. Using rigorous theoretical analysis, we illustrate how the hybrid parallel technique based on multiplicative calculus achieves a remarkable convergence order of 12, indicating its effectiveness and efficiency in solving complex nonlinear equations. The intrinsic stability and consistency of the approach—when applied to nonlinear situations—are clearly indicated by the symmetry seen in the dynamical planes for various parameter values. The method’s symmetrical behavior indicates that it produces accurate findings under a range of scenarios. Using a dynamical system procedure, the ideal parameter values are systematically analyzed in order to further improve the method’s performance. Implementing the aforementioned parameter values using the parallel approach yields very reliable and consistent outcomes. The method’s effectiveness, reliability, and consistency are evaluated through the analysis of numerous nonlinear engineering problems. The analysis provides a detailed comparison with current techniques, emphasizing the benefits and potential improvements of the novel approach.

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Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Cited by 3 publications

References 10 publications

A Numerical Method using Collocation Approach for the Solution of Volterra-Fredholm Integro-Differential Equations

A Numerical Method using Collocation Approach for the Solution of Volterra-Fredholm Integro-Differential Equations

Numerical simulation of Volterra PIDE with singular kernel via modified cubic exponential and uniform algebraic trigonometric tension B-spline DQM

On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations

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