Conformable non-polynomial spline method: A robust and accurate numerical technique

Yousif, Majeed A.; Hamasalh, Faraidun K.

doi:10.1016/j.asej.2023.102415

Cited by 5 publications

(1 citation statement)

References 46 publications

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“…In recent years, numerous authors have proposed various methods to numerically solve the time-fractional Fisher equation, including conformable fractional derivatives and different types of fractional derivatives [4][5][6][7][8][9][10][11]. The exponential finite difference method we employ has not been previously utilized for solving fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

İnan

2024

Symmetry

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This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method to solve this equation, considering the conformable fractional derivative. Furthermore, we analyze the stability of the method through theoretical considerations. The method involves transforming the problem into systems of nonlinear equations at each time since our method is an implicit method, which is then solved by converting them into linear equations systems using the Newton method. To test the accuracy of the method, we compare the results obtained with exact solutions and with those available in the literature. Additionally, we examine the symmetry of the graphs obtained from the solution to examine the results. The findings of our numerical simulations demonstrate the effectiveness and reliability of the proposed approach in solving the generalized fractional-order Fisher equation.

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Section: Introductionmentioning

confidence: 99%

The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

İnan

2024

Symmetry

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Finite-Time Partial Component Consensus for Nonlinear Leader-Following Multi-Agent Systems

Yan,

Yang,

Luo

et al. 2024

Mathematics

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The problem of finite-time partial component consensus (FTPCC) for first-order nonlinear multi-agent systems (MASs) is investigated in this paper for the first time. By incorporating the permutation matrix approach, we derive a novel error system for identical components, which facilitates stability analysis. Leveraging partial variable stability theory and related foundational knowledge, we devise two adaptable protocols. These protocols are tailored to achieve FTPCC in nonlinear MASs, one for systems without disturbances and another for those with bounded disturbances. To validate our findings, numerical examples are provided, demonstrating the effectiveness of the proposed results.

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Extension of the First-Order Recursive Filters Method to Non-Linear Second-Kind Volterra Integral Equations

Heyd

2024

Mathematics

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A new numerical method for solving Volterra non-linear convolution integral equations (NLCVIEs) of the second kind is presented in this work. This new approach, named IIRFM-A, is based on the combined use of the Laplace transformation, a first-order decomposition, a bilinear transformation, and the Adomian decomposition. Unlike most numerical methods based on the Laplace transformation, the IIRFM-A method has the dual advantage of requiring neither the calculation of the Laplace transform of the source function nor that of intermediate inverse Laplace transforms. The application of this new method to the case of non-convolutive multiplicative kernels is also introduced in this work. Several numerical examples are presented to illustrate the great flexibility and efficiency of this new approach. A concrete thermal problem, described by a non-linear convolutive Volterra integral equation, is also solved numerically using the new IIRFM-A method. In addition, this new approach extends for the first time the field of use of first-order recursive filters, usually restricted to the case of linear ordinary differential equations (ODEs) with constant coefficients, to the case of non-linear ODEs with variable coefficients. This extension represents a major step forward in the field of recursive filters.

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Conformable non-polynomial spline method: A robust and accurate numerical technique

Cited by 5 publications

References 46 publications

The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation

Finite-Time Partial Component Consensus for Nonlinear Leader-Following Multi-Agent Systems

Extension of the First-Order Recursive Filters Method to Non-Linear Second-Kind Volterra Integral Equations

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