Implicit One-Step Legendre Polynomial Hybrid Block Method for the Solution of First-Order Stiff Differential Equations

We formulate an implicit hybrid block method for the numerical solution of stiff first-order Ordinary Differential Equations (ODEs) using the Legendre polynomial as our basis function via interpolation and collocation techniques. The paper further investigates the basic properties of the implicit hybrid block method and found it to be zero-stable, consistent and convergent. The method was also tested on some sampled stiff problems and found to perform better than some existing ones with which we compared our results.