Abstract
A numerical study of the solution of boundary value problems with the tridiagonal matrix approach has been done. The case studied is computing the electrical potential expressed by 1D Poisson’s equation with boundary conditions. The 1D Poisson’s equation are then discreted with the finite different method so as to form a system of linier equations. The system of non homogeneous linear equations that can be formed is a tridiagonal matrix. Then the matrix is solved by Gaussian elimination algorithm. On this study, the algorithm is implemented on three programming languages namely, Fortran, Java and MATLAB.
Highlights
Masalah syarat batas sering muncul pada persamaan diferensial baik persamaan diferensial biasa ataupun persamaan diferensial parsial yang merupakan pondasi kajian ilmu-ilmu fisika terapan
The matrix is solved by Gaussian elimination algorithm
The algorithm is implemented on three programming languages namely, Fortran, Java and MATLAB
Summary
Medan listrik yang menembus suatu permukaan khayal dapat dijelaskan oleh hukum Gauss dalam bentuk diferensial dinyatakan sebagai :. Medan listrik E adalah gradien potensial istrik φ dinyatakan oleh ungkapan :. Dikarenakan operator nabla ∇ adalah vektor maka dapat disederhanakan sehingga berbentuk. Bentuk matematis persamaan (3) dikenal dengan Persamaan Poisson. Jika ruas kanan persamaan Poisson bernilai nol persamaan akan. BINA TEKNIKA, Volume 13 Nomor 1, Edisi Juni 2017, 59-64 mereduksi menjadi persamaan Laplace seperti berikut,. Persamaan Laplace dapat ditemukan di banyak fenomena seperti aliran fluida, elektrostatika, gelombang elektromagnetika dan aliran panas. Bentuk umum persamaan Poisson 1D secara matematis tidak lain adalah persaman diferensial berbentuk :. Dapat diperoleh jika kondisi batas y(x) diketahui
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