armancodv / tdma

In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.

TDMA (Tridiagonal matrix algorithm)

In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as

where and .

Install

npm install tdma

Sample Code

Using coefficientMatrix

const tdma = require('tdma');

const coefficientMatrix = [
    [2, 3, 0, 0],
    [6, 3, 9, 0],
    [0, 2, 5, 2],
    [0, 0, 4, 3]
];
const rigthHandSideVector = [21, 69, 34, 22];

const answer = tdma.solver(coefficientMatrix, rigthHandSideVector);
console.log(answer);

Using Diagonals

const tdma = require('tdma');

const a = [0, 6, 2, 4];
const b = [2, 3, 5, 3];
const c = [3, 9, 2, 0];
const d = [21, 69, 34, 22];

const answer = tdma.tdma(a, b, c, d);
console.log(answer);

Method

The forward sweep consists of modifying the coefficients as follows, denoting the new coefficients with primes:

and

The solution is then obtained by back substitution:

The method above preserves the original coefficient vectors. If this is not required, then a much simpler form of the algorithm is

followed by the back substitution

Reference: https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm