Local radial basis function–finite-difference method to simulate some models in the nonlinear wave phenomena: regularized long-wave and extended Fisher–Kolmogorov equations

Dehghan, Mehdi; Shafieeabyaneh, Nasim

doi:10.1007/s00366-019-00877-z

Cited by 36 publications

(7 citation statements)

References 59 publications

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“…Nikan et al solved numerically the nonlinear KdV-Benjamin-Bona-Mahony-Burgers (KdV-BBM-B) with the help of the RBF-PS [58]. Dehghan and Shafieeabyaneh addressed the RLW and extended Fisher-Kolmogorov (EFK) equations using local meshless RBF-FD [59]. Ebrahimijahan and Dehghan proposed a numerical technique for solving the nonlinear generalized BBBM-B and RLW equations based on the integrated RBF [60].…”

Section: The Rbf-fd Collocation Methodsmentioning

confidence: 99%

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

2020

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This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.

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Section: The Rbf-fd Collocation Methodsmentioning

confidence: 99%

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

2020

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“…wherein, φ is the radial function; λ i is the weight at i; and d oi is the Euclidean distance between the unknown point s o and known point s i . In this study, the linear radial function was utilized for all interpolations, and is given as [27]:…”

Section: Radial Basis Function (Rbf)mentioning

confidence: 99%

Impacts of Spatial Interpolation Methods on Daily Streamflow Predictions with SWAT

Felix¹,

Jung²

2022

Water

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Precipitation is a significant input variable required in hydrological models such as the Soil & Water Assessment Tool (SWAT). The utilization of inaccurate precipitation data can result in the poor representation of the true hydrologic conditions of a catchment. SWAT utilizes the conventional nearest neighbor method in assigning weather parameters for each subbasin; a method inaccurate in representing spatial variations in precipitation over a large area, with sparse network of gauging stations. Therefore, this study aims to improve the spatial variation in precipitation data to improve daily streamflow simulation with SWAT, even pre-model calibration. The daily streamflow based on four interpolation methods, nearest neighbor (default), inverse-distance-weight, radial-basis function, and ordinary kriging, were evaluated to determine which interpolation method is best represents the precipitation at Yongdam watershed. Based on the results of this study, the application of spatial interpolation methods generally improved the performance of SWAT to simulate daily streamflow even pre-model calibration. In addition, no universal method can accurately represent the long-term spatial variation of precipitation at the Yongdam watershed. Instead, it was observed that the optimal selection of interpolation method at the Yongdam watershed is dependent on the long-term climatological conditions of the watershed. It was also observed that each interpolation method was optimal based on certain meteorological conditions at Yongdam watershed: nearest neighbor for cases when the occurrence probability of extreme precipitation is high during wet to moderately wet conditions; radial-basis function for cases when the number of dry days were high, during wet, severely dry, and extremely dry conditions; and ordinary kriging or inverse-weight-distance method for dry to moderately dry conditions. The methodology applied in this study improved the daily streamflow simulations at Yongdam watershed, even pre-model calibration of SWAT.

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“…Momani and Yıldırım in [24] have obtained the approximate analytical solution of CDE via He's homotopy perturbation method. Since the analytical solution of fractional-order problems in most of the cases is difficult to obtain, the researchers have developed numerous numerical methods for the investigation of the solutions of fractional-order problems such as the finite difference method [25], finite element method [26], finite volume method [27], and meshless methods [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

“…Oruç [11] applied the meshfree method based on finite differences for the numerical solution of Zakharov-Rubenchik equations. Dehghan and Shafieeabyaneh [29] utilized the RBF method based on finite difference to simulate the regularized long-wave equation (RLWE) and extended Fisher-Kolmogorov equation (EFKE) in higher dimensions. Mohebbi et al [14] investigated the solution of 2D modified anomalous sub-diffusion equation of arbitrary order via the RBF method.…”

Section: Introductionmentioning

confidence: 99%

On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations

Kamran

Kamal

Rahmat

et al. 2021

Mathematical Problems in Engineering

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In this paper, we present an efficient method for the numerical investigation of three-dimensional non-integer-order convection-diffusion equation (CDE) based on radial basis functions (RBFs) in localized form and Laplace transform (LT). In our numerical scheme, first we transform the given problem into Laplace space using Laplace transform. Then, the local radial basis function (LRBF) method is employed to approximate the solution of the transformed problem. Finally, we represent the solution as an integral along a smooth curve in the complex left half plane. The integral is then evaluated to high accuracy by a quadrature rule. The Laplace transform is used to avoid the classical time marching procedure. The radial basis functions are important tools for scattered data interpolation and for solving partial differential equations (PDEs) of integer and non-integer order. The LRBF and global radial basis function (GRBF) are used to produce sparse collocation matrices which resolve the issue of the sensitivity of shape parameter and ill conditioning of system matrices and reduce the computational cost. The application of Laplace transformation often leads to the solution in complex plane which cannot be generally inverted. In this work, improved Talbot’s method is utilized which is an efficient method for the numerical inversion of Laplace transform. The stability and convergence of the method are discussed. Two test problems are considered to validate the numerical scheme. The numerical results highlight the efficiency and accuracy of the proposed method.

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Local radial basis function–finite-difference method to simulate some models in the nonlinear wave phenomena: regularized long-wave and extended Fisher–Kolmogorov equations

Cited by 36 publications

References 59 publications

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Impacts of Spatial Interpolation Methods on Daily Streamflow Predictions with SWAT

On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations

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