The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation

Rasoulizadeh, Mohammad Navaz; Nikan, O.; Avazzadeh, Z.

doi:10.1007/s40096-021-00375-8

Cited by 27 publications

(8 citation statements)

References 40 publications

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“…ere are many RBFs (expression of φ ) available in literature such as Multiquadric (MQ), Inverse Multiquadric (IMQ), Gaussian, in Plate spline [27][28][29][30][31][32][33][34] etc.…”

Section: Rbfs and Local Rbf-fd Approximationmentioning

confidence: 99%

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Jiwari

Singh

2022

Journal of Mathematics

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This work analyze singularly perturbed convection-diffusion-reaction (CDR) models with two parameters and variable coefficients by developing a mesh-free scheme based on local radial basis function-finite difference (LRBF-FD) approximation. In the evolvement of the scheme, time derivative is discretized by forward finite difference. After that, LRBF-FD approximation is used for spatial discretization, and we obtained a system of linear equations. Then, the obtained linear system is solved by LU decomposition method in MATLAB. For numerical simulation, four singularly perturbed models are pondered to check the efficiency and chastity of the proposed scheme.

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“…ere are many RBFs (expression of φ ) available in literature such as Multiquadric (MQ), Inverse Multiquadric (IMQ), Gaussian, in Plate spline [27][28][29][30][31][32][33][34] etc.…”

Section: Rbfs and Local Rbf-fd Approximationmentioning

confidence: 99%

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Jiwari

Singh

2022

Journal of Mathematics

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“…The meshfree RBF method is used in both local and global forms. Some authors have tried localized-RBF-based strategies, such as the localized-RBF-generated FD (RBF-FD) [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and the RBF partition of unity (RBF-PU) [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

Section: Properties Of Rbfsmentioning

confidence: 99%

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Golbabai

Safaei

Molavi-Arabshahi

2022

Entropy

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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

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“…Recently, some advantages of the local RBF‐FD were considered in comparison with the FD and RBF schemes 45–50 . Bayona et al 50 implemented the Maple software and obtained formulae for the RBF‐FD coefficients of the MQ function when the operator L is the first‐ or second‐order derivatives.…”

Section: Spatial Discretizationmentioning

confidence: 99%

Localized kernel‐based meshless method for pricing financial options underlying fractal transmission system

Nikan

Avazzadeh

Machado

2021

Math Methods in App Sciences

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The variation in the option pricing of the fractal transmission system is modelled by the time fractional Black–Scholes equation (TFBSE). This paper proposes an efficient local meshless method for the numerical simulation of the TFBSE. At the first step, a difference formula of L1 type is employed to get a semi‐discrete algorithm in the temporal variable with a accuracy of order 2 − α in the case of smooth solutions, where 0 < α ≤ 1 is the fractional‐order derivative. At the second step, a localized radial basis function finite difference is adopted to derive a full‐discrete scheme. Moreover, the unconditional stability and convergence of the proposed method are analyzed based on energy norm. The exact expressions for the weights of the first and second derivatives are used by imposing a multiquadric function generated by finite difference. The proposed technique produces linear systems with tridiagonal and diagonal matrices. Numerical experiments highlight the performance of the method.

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The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation

Cited by 27 publications

References 40 publications

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Localized kernel‐based meshless method for pricing financial options underlying fractal transmission system

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