TABLE OF CONTENTS In this chapter we will consider boundary value problems for ordinary differential equations and for partial differential equations. Mathcad's tools enable you to solve boundary value problems for systems of ordinary differential equations, where part of the boundary conditions are set at the starting point of the interval, and the remaining conditions are set at its ending point ( see Section 12.1). Furthermore, it is also possible to solve equations with boundary conditions specified at some internal point of the interval. Mathcad provides appropriate built-in functions for solving boundary value problems. These functions implement the shooting method algorithm ( see Section 12.1.2).
Boundary value problems for most practical applications often depend on some numeric parameter. In this case, the solution exists only for some countable number of parameter values rather than for all its values. Such problems are also known as eigenvalue problems ( see Section 12.2).
Despite the fact that while in contrast to Cauchy problems for ordinary differential equations, Mathcad doesn't provide built-in functions for solving stiff boundary value problems, these problems can still be solved using difference scheme programming ( see Section 12.3). Possible variations of difference scheme implementations are also provided for some boundary value problems with partial differential equations. Furthermore, some particular cases of partial differential equations, such as Poisson's equations, can even be solved using built-in functions provided by Mathcad ( see Section 12.4).
Formulation of the boundary value problems...
