A new optimization method for a class of time fractional convection-diffusion-wave equations with variable coefficients

2017 ◽  
Vol 132 (3) ◽  
Author(s):  
M. Sh. Dahaghin ◽  
H. Hassani
Keyword(s):  
Wave Equations ◽  
Optimization Method ◽  
Variable Coefficients ◽  
Diffusion Wave ◽  
Convection Diffusion

Numerical simulation of higher-order diffusion-wave equations of variable coefficients using the meshless spectral method

2020 ◽  
pp. 2150010
Author(s):  
Manzoor Hussain ◽  
Sirajul Haq
Keyword(s):  
Wave Equations ◽  
Interpolation Method ◽  
Variable Coefficients ◽  
Higher Order ◽  
Implicit Time ◽  
Test Problems ◽  
Time Step ◽  
Diffusion Wave ◽  
Time Step Size ◽  
Time Stepping

In this paper, meshless spectral interpolation technique using implicit time stepping scheme is proposed for the numerical simulations of time-fractional higher-order diffusion wave equations (TFHODWEs) of variable coefficients. Meshless shape functions, obtained from radial basis functions (RBFs) and point interpolation method (PIM), are used for spatial approximation. Central differences coupled with quadrature rule of [Formula: see text] are employed for fractional temporal approximation. For advancement of solution, an implicit time stepping scheme is then invoked. Simulations performed for different benchmark test problems feature good agreement with exact solutions. Stability analysis of the proposed method is theoretically discussed and computationally validated to support the analysis. Accuracy and efficiency of the proposed method are assessed via [Formula: see text], [Formula: see text] and [Formula: see text] error norms as well as number of nodes [Formula: see text] and time step-size [Formula: see text].

scholarly journals Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1696
Author(s):  
A. S. Hendy ◽  
R. H. De Staelen
Keyword(s):  
Wave Equations ◽  
Order Reduction ◽  
Fixed Time ◽  
Difference Approximation ◽  
Discrete Energy ◽  
Diffusion Wave ◽  
Convection Diffusion ◽  
Convergence And Stability ◽  
Order Scheme ◽  
Equations With Delay

In this paper, we introduce a high order numerical approximation method for convection diffusion wave equations armed with a multiterm time fractional Caputo operator and a nonlinear fixed time delay. A temporal second-order scheme which is behaving linearly is derived and analyzed for the problem under consideration based on a combination of the formula of L2−1σ and the order reduction technique. By means of the discrete energy method, convergence and stability of the proposed compact difference scheme are estimated unconditionally. A numerical example is provided to illustrate the theoretical results.

Exact Difference Schemes for Time-dependent Problems

2005 ◽  
Vol 5 (4) ◽  
pp. 422-448 ◽  
Author(s):  
P Matus ◽  
U. Irkhin ◽  
M. Lapinska-Chrzczonowicz
Keyword(s):  
Wave Equations ◽  
Variable Coefficients ◽  
Transport Equations ◽  
Difference Schemes ◽  
Quasilinear Parabolic Equations ◽  
Convection Diffusion ◽  
Moving Grids ◽  
Exact Difference ◽  
Rectangular Grids ◽  
Time Dependent Problems

AbstractFor one-dimensional and multidimensional semilinear transport equations of quite a general form with given initial data and boundary conditions the exact difference schemes (EDSs) are constructed. In the case of constant coe±cients, such numerical methods can be created on rectangular grids, while in the case of variable coefficients - on moving grids only. The questions of developing difference schemes of arbitrary order for quasi-linear transport equations with a nonlinear right-hand side are discussed. In this paper, the EDSs are constructed also for certain classes of linear and quasilinear parabolic equations, for convection-diffusion problems with a small parameter, as well as inhomogeneous wave equations with constant coe±cients.

scholarly journals Approximate Solutions of Time Fractional Diffusion Wave Models

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 923 ◽  
Author(s):  
Abdul Ghafoor ◽  
Sirajul Haq ◽  
Manzoor Hussain ◽  
Poom Kumam ◽  
Muhammad Asif Jan
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Quadrature Rule ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Haar Wavelets ◽  
Test Problems ◽  
Algebraic Equations ◽  
Diffusion Wave ◽  
Wave Models

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

scholarly journals Novel finite point approach for solving time-fractional convection-dominated diffusion equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaomin Liu ◽  
Muhammad Abbas ◽  
Honghong Yang ◽  
Xinqiang Qin ◽  
Tahir Nazir
Keyword(s):  
Variable Coefficients ◽  
Numerical Dispersion ◽  
Discrete Equation ◽  
Finite Point ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Tailored Finite Point Method ◽  
L1 Approximation ◽  
The Stability

AbstractIn this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

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