Numerical Results of Crank-Nicolson and Implicit Schemes to Laplace Equation with Uniform and Non-Uniform Grids
Abstract In this paper, we investigate the numerical results between Implicit and Crank-Nicolson method for Laplace equation. Based on the numerical results obtained, we get the conclusion that the absolute error of Crank-Nicolson method is smaller than the absolute error of Implicit method for unif...
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| Format: | Article |
| Language: | English |
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UIN Syarif Hidayatullah
2021-11-01
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| Series: | InPrime |
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| Online Access: | https://journal.uinjkt.ac.id/index.php/inprime/article/view/20917 |
| Summary: | Abstract
In this paper, we investigate the numerical results between Implicit and Crank-Nicolson method for Laplace equation. Based on the numerical results obtained, we get the conclusion that the absolute error of Crank-Nicolson method is smaller than the absolute error of Implicit method for uniform and non-uniform grids which both refer to the analytical solution of Laplace equation obtained by separable variable method.
Keywords: Crank-Nicolson; Implicit; Laplace equation; separable variable method; uniform and non-uniform grids.
Abstrak
Dalam makalah ini, kami menyelidiki hasil numerik antara etode Implisit dan Crank-Nicolson untuk persamaan Laplace. Berdasarkan hasil numerik yang diperoleh, kita mendapatkan kesimpulan bahwa kesalahan absolut metode Crank-Nicolson lebih kecil daripada kesalahan absolut metode Implisit untuk grid seragam dan tak-seragam yang keduanya mengacu pada solusi analitik persamaan Laplace yang diperoleh dengan metode separable.
Kata kunci: Crank-Nicolson; Implisit; persamaan Laplace; metode variable terpisah; grid seragam dan tak-seragam. |
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| ISSN: | 2686-5335 2716-2478 |