Variable Step Variable Order Block Backward Differentiation Method for Solving Stiff Ordinary Differential Equation

Abstract

Block backward differentiation formula with variable step variable order approach (VSVO) for solving stiff ordinary differential equations (ODE) is described in this project. The detailed algorithms of VSVO-BBDF method is discussed to show the crucial part of the order and stepsize selections prior to getting the numerical results the matlab suit of ODEs solvers namely odes15s and odes23s is applied for the numerical comparison purposes. Meanwhile the consistency and zero stability properties that lead to the convergence of the method of order three up to five, as well as the strategies in choosing the order and the stepsize are elaborated. Similarly numerical results are obtained after a fair comparison is made between VSVO-BBDF (2) and stiff ODEs solvers in matlab. In conclusion, the results display positive trends in reducing the total numbers of steps and increasing the accuracy of the approximations. The results also shows that VSVOBBDF method reduces the time excussion for solving first order stiff ODEs as compared to matlab. Therefore the methods serve the purpose of significant alternatives for solving stiff ODE.