More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI)

Shivanian, Elyas; Jafarabadi, Ahmad

doi:10.1016/j.enganabound.2016.08.006

Cited by 28 publications

(10 citation statements)

References 33 publications

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“…According to Jiao et al [21], "although the series can be rapidly convergent in a very small region, it has very slow convergence rate in the wider region and the truncated series solution is an inaccurate solution in that region, which will greatly restrict the application area of the method". Moreover, the BVP (1), (2) has been analyzed by meshless method through radial basis functions, though they are often used for high-dimensional problems [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The interested readers are also referred to [36][37][38][39] for other useful techniques, which can be applied for the same problems.…”

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Shivanian

Ansari

2019

Acta Phys. Pol. A

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In current work, a novel intelligent computational technique is adopted for searching the behaviour of the problem of buckling of nano-actuators in the presence of various nonlinear forces. In order to accomplish this aim, the governing integro-differential equation in general form is taken into account for nano-actuators, which contains various nonlinear forces as well. This generalized form for the nano-actuators is in fact a non-linear fourth-order Fredholm integro-differential boundary value problem. The boundary value problem is transformed into an equivalent problem whose boundary conditions are such that it is convenient to apply reformed version of the Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an uninspected error which is minimized through adjusting weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. This numerical technique enables us to overcome all kind of nonlinearities in the mentioned boundary value problem, and then to obtain an accurate solution. Thus, it can expedite the design of nano-actuators.

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Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Shivanian

Ansari

2019

Acta Phys. Pol. A

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“…In the proposed technique, the radial point interpolation functions are locally constructed and used as the shape functions and also the appearing high-order derivative operators in the governing equation are approximated by using sparse operational matrices. Shivanian and Jafarabadi have successfully formulated and implemented the local spectral meshless radial point interpolation method for solving inverse elliptic Cauchy problems, 55 two-dimensional nonlinear generalized Benjamin-Bona-Mahony-Burgers 56 and pseudoparabolic equations in two spatial dimensions. 57 Moreover, several strategies have been proposed and pursued for the temporal discretization of time dependent fractional order models, for example, finite difference methods, method of line (MOL), 58 Laplace transformation and spectral collocation schemes.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a generalized anomalous electro‐diffusion process in nerve cells by a localized meshless approach in Pseudospectral mode

Ghehsareh

Seidzadeh

Etesami

2020

Int J Numerical Modelling

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Pseudospectral techniques are known as powerful tools and highly accurate solvers to deal with partial differential equations. In the current work, a local meshless technique in Pseudospectral mode is employed to deal with an interesting and general mathematical model which describes anomalous electrodiffusion of ions in spiny dendrites, the two-dimensional variable-order time fractional nonlinear cable equation. For this purpose, at first step a second-order implicit difference method and a modified second-order weighted and shifted Grünwald difference scheme are used to discretize the appearing integer and variable order fractional time derivatives, respectively. Then a local Pseudospectral meshless method based on the sufficiently smooth compactly supported radial point interpolation basis functions is formulated for solving the semidiscretized problem. The main advantage of the proposed computational technique is that it leads to a sparse and better-conditioned system of algebraic equations. Finally, some numerical experiments are presented to demonstrate and verify the performance and accuracy of the method.

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“…In special case, if = 0, = 1 and = −1 then the problem acquired to the regularized long-wave equation (RLWE) that was studied as an improvement of the Korteweg-de Vries (KdV) equation for modeling long surface gravity waves. Various methods (analytical and numerical) have been applied for solving the BBMB equation [32][33][34][35][36][37][38][39]. Our goal is to deal with the GBBMB through the SBM in order to acquire more accurate results in comparison with other methods.…”

Section: Introductionmentioning

confidence: 99%

Meshless formulation to two‐dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence

Aslefallah

Abbasbandy

Shivanian

2019

Numerical Methods Partial

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In this study, the singular boundary method (SBM) is employed for the simulation of nonlinear generalized Benjamin–Bona–Mahony–Burgers problem with initial and Dirichlet‐type boundary conditions. The θ‐weighted finite difference method is used to discretize the time derivatives. Then the original equations are split into a system of partial differential equations. A splitting scheme is applied to split the solution of the inhomogeneous governing equation into homogeneous solution and particular solution. To solve this system, the method of particular solution (MPS) in combination with the SBM is used where the SBM is used for homogeneous solution and MPS is used for particular solution. Furthermore, the stability and convergence of the proposed method is conducted. Finally, several numerical examples with different domains are provided and compared with the exact analytical solutions to show the accuracy and efficiency in comparison with existing other methods.

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More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI)

Cited by 28 publications

References 33 publications

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Numerical simulation of a generalized anomalous electro‐diffusion process in nerve cells by a localized meshless approach in Pseudospectral mode

Meshless formulation to two‐dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence

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