Construction of Adaptive Multistep Methods for Problems with Discontinuities, Invariants, and Constraints
The wide variety of physical phenomena, such as motion of objects, reaction among chemical substances, electricity flow in a circuit can be described by equations with quantities that vary along time.The rate at which a quantity is changing with respect to its independent variable (time), is represented by its derivative. Thus, these phenomena are modeled by equations with differential variables tAdaptive multistep methods have been widely used to solve initial value problems. These ordinary differential equations (ODEs) may arise from semi-discretization of time-dependent partial differential equations(PDEs) or may combine with some algebraic equations to represent a differential algebraic equations (DAEs).In this thesis we study the initialization of multistep methods and parametrize som
