Optimal solution techniques for control problem of evolution equations

A lot of optimal solution techniques exist in literature and have been employed to solve optimization problems. However, in this work, two optimal solution techniques namely the Steepest Descent Method (SDM) and the Extended Conjugate Gradient Method (ECGM) were applied to two evolution equations to determine which best approximates the system to its analytic solution. Comparisons were also carried out between the SDM and the ECGM for optimal solution and convergence. In doing so, the Liberty Basic Programming Language (LBPL) was employed to perform various numerical iterations on the respective algorithms of the techniques. It was discovered that the SDM proved to be a better technique in obtaining an optimal solution than the ECGM.