INVESTIGATE A RANGE OF NUMERICAL IMPLICIT METHODS FOR SOLVING STIFF DIFFERENTIAL EQUATIONS

Abstract

The phenomena of stiffness and general-purpose methods for solving stiff differential equations are the primary topics of this investigation. We are attempting to characterize the distinct features of stiff differential equations as well as the precise location of the problem. A numerical technique is required since analytical solutions do not exist for the majority of practical stiff systems. Numerous computer programs such as DIFSUB, GEAR, EPISODE, and others provide implementations of these methods. For ordinary differential equations, the backward differentiation formulas (BDFs) are the go-to tools for solving tough starting value issues. This study focuses on EPISODE, an extremely efficient algorithm, using a variable-coefficient backward differentiation formula as its foundation. Even though the strategy is generally effective, our research reveals that novice users may encounter difficulties in some areas. All of those issues have been identified, and solutions are being suggested for future revisions.