Convergence Analysis of Stiff Ordinary Differential Equations Solver via Singly Diagonally Implicit 2-Point Block Multistep Formula

Saufianim Jana Aksah, Zarina Bibi Ibrahim, Khairil Iskandar Othman

A new numerical solver of 2-point singly diagonally implicit block multistep formula (SDI2BMF) for stiff ordinary differential equations (ODEs) is proposed. The SDI2BMF method introduced is developed in lower triangular matrix with identical diagonal constants. This will result in only single Jacobian estimation and one LU decomposition for each step. Convergence analysis is conducted to validate the ability of the method to estimated solution of an ODE to any required precision. Essential conditions for the proposed method to converge involving order, zero stability and consistency are further studied. Efficiency of the SDI2BMF method is measured based on its accuracy to solve for various type of stiff ODEs. Numerical experiment proved that the SDI2BMF method has better performances than the existing solvers.

Volume 11 | 12-Special Issue

Pages: 155-163