Numerical Results of Crank-Nicolson and Implicit Schemes to Laplace Equation with Uniform and Non-Uniform Grids

Abstract

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.

Keywords

• crank-nicolson
• implicit
• laplace equation
• separable variable method.