Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation

Msmali, Ahmed Hussein; Tamsir, Mohammad; Ahmadini, Abdullah Ali H.

doi:10.1016/j.asej.2021.04.004

Cited by 15 publications

(3 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sheng [43] used Runge-Kutta techniques with compact Difference methods for solving the unsteady Euler equations. Tamsir et al [48][49][50][51][52][53][54][55][56] solved various nonlinear partial differential equations using modified cubic B-spline DQM (MCB-DQM), in space to transform the system of partial differential equations (PDE) to system of ordinary differential equations (ODE). The solution is completed by employing a five stage and fourth-order strong stability preserving Runge-Kutta algorithm, in time (SSP-RK54).…”

Section: Introductionmentioning

confidence: 99%

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

M. Salah,

M. S. Matbuly,

O. Civalek

et al. 2024

AAMM

View full text Add to dashboard Cite

In this study, a (3+1) dimensional unstable gas flow system is applied and solved successfully via differential quadrature techniques based on various shape functions. The governing system of nonlinear four-dimensional unsteady Navier-Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, Runge-Kutta 4th order method is employed to solve the resulting system of equations. To obtain the solution of this equation, a MATLAB code is designed. The validity of these techniques is achieved by the comparison with the exact solution where the error reach to ≤ 1×10 −5 . Also, these solutions are discussed by seven various statistical analysis. Then, a parametric analysis is presented to discuss the effect of adiabatic index parameter on the velocity, pressure, and density profiles. From these computations, it is found that Discrete singular convolution based on Regularized Shannon kernels is a stable, efficient numerical technique and its strength has been appeared in this application. Also, this technique can be able to solve higher dimensional nonlinear problems in various regions of physical and numerical sciences.

show abstract

Section: Introductionmentioning

confidence: 99%

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

M. Salah,

M. S. Matbuly,

O. Civalek

et al. 2024

AAMM

View full text Add to dashboard Cite

show abstract

“…More recently, Haar wavelet collocation (Asif et al, 2020), CN-DQM and cubic exponential B-splines based scheme (Tamsir and Ahmadini, 2021), Barycentric rational interpolation and LRBFs based numerical algorithms (Jiwari, 2021), ADI spectral element method (Saffarian and Mohebbi, 2021), DQM based methods (Pandit et al, 2017;Alshomrani et al, 2017;Verma and Jiwari, 2015;Jiwari, 2015;Kumar et al, 2013;Jiwari et al, 2012a, b, c;Dehghan and Shokri, 2009) etc., have been developed for these types of models. Such types of models are solved in refs (Oruç, 2021;Kara and € Unsal, 2022;Babu et al, 2021;Ahmad et al, 2021;Turkyilmazoglu, 2010Turkyilmazoglu, , 2014Turkyilmazoglu, , 2017Turkyilmazoglu, , 2018Turkyilmazoglu, , 2019.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Haar wavelet collocation (Asif et al. , 2020), CN-DQM and cubic exponential B-splines based scheme (Tamsir and Ahmadini, 2021), Barycentric rational interpolation and LRBFs based numerical algorithms (Jiwari, 2021), ADI spectral element method (Saffarian and Mohebbi, 2021), DQM based methods (Pandit et al. , 2017; Alshomrani et al.…”

Section: Introductionmentioning

confidence: 99%

Meshfree algorithms for analysis and computational modeling of multidimensional hyperbolic wave models

Pandit,

Verma,

Kumar

et al. 2023

View full text Add to dashboard Cite

PurposeThis article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).Design/methodology/approachIn the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.FindingsFor simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.Originality/valueThe developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

show abstract

Numerical solution of one-dimensional nonlinear Sine–Gordon equation using LOOCV with exponential B-spline

Rani,

Arora,

Bala

2024

Comp. Appl. Math.

View full text Add to dashboard Cite

Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation

Cited by 15 publications

References 40 publications

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

Meshfree algorithms for analysis and computational modeling of multidimensional hyperbolic wave models

Numerical solution of one-dimensional nonlinear Sine–Gordon equation using LOOCV with exponential B-spline

Contact Info

Product

Resources

About