Residual method for nonlinear system of initial value problems

In this thesis, non-linear system of initial value problems are solved numerically using Residual Method which is based on the minimization of a residual function using the Taylor's series expansion. The convergence of the method applied to non-linear system of initial value problems is analysed. The method is illustrated with Lorenz system, which is a chaotic initial value system, and primary HIV-1 infection problem, which is a non-linear dynamical system.