Time and spatial discretization methods that preserve passivity properties for systems described by partial differential equations

2000 ◽  
Author(s):  
D. Kristiansen ◽  
O. Egeland
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Spatial Discretization ◽  
Partial Differential ◽  
Discretization Methods

scholarly journals Numerical Simulation of Partial Differential Equations via Local Meshless Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 257 ◽  
Author(s):  
Imtiaz Ahmad ◽  
Muhammad Riaz ◽  
Muhammad Ayaz ◽  
Muhammad Arif ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Meshless Method ◽  
Three Dimensional ◽  
Salient Feature ◽  
Test Problems ◽  
Spatial Discretization ◽  
Partial Differential ◽  
Meshless Collocation

In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain and also far less sensitive to the variation of shape parameter as compared to the global meshless method (GMM). Both rectangular and non rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy and ease implementation of the proposed method are shown via test problems.

scholarly journals Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
B. A. Jacobs ◽  
C. Harley
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Hybrid Methods ◽  
Test Problems ◽  
Spatial Discretization ◽  
Chebyshev Collocation Method ◽  
Partial Differential ◽  
Chebyshev Collocation

A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.

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