Sinc Collocation Method for Solving Nonlinear Parabolic Partial Differential Equations With Dirichlet Boundary Conditions Using Exponential Transformations
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| Publicado no: | ProQuest Dissertations and Theses (2025) |
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| 100 | 1 | |a Odeh, Moayad | |
| 245 | 1 | |a Sinc Collocation Method for Solving Nonlinear Parabolic Partial Differential Equations With Dirichlet Boundary Conditions Using Exponential Transformations | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a We present a Sinc Collocation Method (SCM) with Double Exponential (DE) transformations for non-linear parabolic partial differential equations (PDEs) on a bounded interval. For the time discretization, we use Crank-Nicolson (C-N) method for the linear part and Heun's method for the nonlinear part and observe second-order accuracy. In the spatial dimension we use Sinc collocation, which promises exponential order convergence for smooth decaying functions on the real line. The DE transformation allows this promise to be realized on a finite interval by mapping it to the real line. The transformation concentrates the collocation points near the ends of the interval, which allows the method to achieve high accuracy and order both at the collocation points and between them.We compare SCM with various existing methods across a range of nonlinear parabolic PDEs with Dirichlet boundary conditions, such as Burgers' equation and several Reaction-Diffusion Equations (RDEs). For Burgers' equation with homogeneous Dirichlet boundary conditions, we mainly compare the SCM with a Hybrid Sinc-Finite Difference Method. Numerical tests confirms SCM's superior performance across various initial conditions and discretization settings. In particular, we show that the hybrid method has much larger errors between collocation points due to Runge's phenomenon. As expected, for non-smooth initial conditions the SCM-DE method only has first order convergence in space. For RDEs with non-homogeneous boundary conditions, we show that SCM is more accurate than several existing methods. Our result highlight SCM's efficiency and accuracy in handling various nonlinear problems. | |
| 653 | |a Mathematics | ||
| 653 | |a Engineering | ||
| 653 | |a Applied mathematics | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3226001722/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3226001722/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |