Therefore, this iterative method can be used because it automatically becomes a diagonally dominant matrix.
\(||\bf M ||<1\) (This is true when diagonally dominant.)Īlthough we don’t explain in detail, in the case of the diffusion equation, the information in cell \(i\) at the current time is effective in the information in cell \(i\) at the next time. It may be used when the element positions are fixed and the calculation can be simplified like the TDMA method, but it is rare.Ī method of performing iterative calculations to converge from an initial vector \(\bf x ^ →0\) The answer is certain, but it requires a lot of storage capacity and takes a long time to calculate. “Gaussian elimination method” (Part 2-2)and “TDMA method” (Part 3-2)are direct solutions. T is a method to obtain a solution by finite number of operations. There are three methods of solving such a matrix: “direct solution method”, “steady iteration method”, and “nonstationary iterative method”. We already know (bf A, bf b) and want to figure out (bf x). And I think it has been understood from the flow up to the previous time that the implicit method can be transformed as follows. In the first place, we are proceeding with the idea of solving with the implicit method in Part 7. In Part 7-3, I would like to explain the solution of the inverse matrix in numerical analysis.
