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| Content Provider | Springer Nature Link |
|---|---|
| Author | Ilati, Mohammad Dehghan, Mehdi |
| Copyright Year | 2016 |
| Abstract | Mathematical modeling of pattern formation in developmental biology leads to non-linear reaction–diffusion systems which are usually highly stiff in both diffusion and reaction terms. In this paper, the Direct Meshless Local Petrov–Galerkin (DMLPG) procedure is applied to find the numerical solution of some non-linear time-dependent reaction–diffusion systems such as Schnakenberg model, Gierer–Meinhardt model, FitzHugh–Nagumo model and Gray–Scott model. As far as we know, it is the first time that DMLPG method is applied for solving non-linear partial differential equations (PDEs) and systems of PDEs. Computational efficiency is the most significant advantage of the DMLPG method in comparison with the classic Meshless Local Petrov–Galerkin (MLPG) method. This is due to the fact that DMLPG shifts the numerical integrations over low-degree polynomials instead of over complicated moving least squares (MLS) shape functions and this reduces the computational costs, significantly. The main aim of this paper is to show that the DMLPG method is also suitable for solving the non-linear time-dependent systems, especially reaction–diffusion systems. Numerical results support the good efficiency of the proposed method for solving non-linear reaction–diffusion systems. Also it is shown that DMLPG provides considerable savings in computational time in comparison with the classical MLPG method. |
| Ending Page | 124 |
| Page Count | 18 |
| Starting Page | 107 |
| File Format | |
| ISSN | 01770667 |
| e-ISSN | 14355663 |
| Journal | Engineering with Computers |
| Issue Number | 1 |
| Volume Number | 33 |
| Language | English |
| Publisher | Springer London |
| Publisher Date | 2016-06-09 |
| Publisher Place | London |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | FitzHugh–Nagumo model ApplicationMathematics/Computational Methods of Engineering Meshless local weak form methods Systems Theory, Control Gray–Scott model Classical Mechanics Schnakenberg model Gierer–Meinhardt model MLPG methods Generalized moving least squares (GMLS) approximation Calculus of Variations and Optimal Control; Optimization Direct MLPG (DMLPG) methods Computer-Aided Engineering (CAD, CAE) and Design Math. Applications in Chemistry |
| Content Type | Text |
| Resource Type | Article |
| Subject | Engineering Computer Science Applications Modeling and Simulation Software |
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