On the numerical solution of certain initial value problems

Higher order time-space elements based on two different formulations (quasi-variational and least square) are used to solve both linear and non-linear problems associated with the parabolic differential equation. Then, a semi-analytical method (similar to the finite strip method in structural ans analysis) is developed to solve similar linear problems. Convergence studies have been carried out for both methods to demonstrate their accuracy. Refs.link_to_subscribed_fulltex