Yazar "Malkhalifeh, Mohsen Rostamy" seçeneğine göre listele

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    A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations
    (Elsevier Ltd, 2024) Savadkoohi, Fateme Rezaei; Rabbani, Mohsen; Allahviranloo, Tofigh; Malkhalifeh, Mohsen Rostamy
    In this article, we construct a fractional multi-wavelet basis based on Legendre polynomials to solve fractional delay linear and nonlinear differential equations. For this we introduce an orthonormal fractional basis for Banach space L2[0,1] with suitable inner product which make it effective to decrease computational operations and increase accuracy to find approximate solution of the equations. Also, solving fractional problems by orthogonal basis such as Legendre polynomials has a lower accuracy in comparison with fractional basis. Finally, some examples are solved to show the high accuracy of the presented method, and also to compare with some other works. © 2024
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    Application of the reproducing kernel method for solving linear Volterra integral equations with variable coefficients
    (Iop Publishing Ltd, 2024) Amoozad, Taher; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.
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    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.
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    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.