ABSTRACT
Most of existing numerical procedures for computing solutions are indirect, fixed-grid and based on Kawarada’s original framework. Such computations are often inefficient and unreliable due to the blow-up singularity involved. This chapter is concerned with a modified adaptive method dealing with such problems. Moving mesh mechanisms are achieved both in space and time. Special monitor functions based on arc-lengths of explosive rate function are derived. The chapter shows that, under proper smoothness constraints, the numerical solution generated converges monotonically to the physical solution.
