A symbolic framework for operations on linear boundary problems

We describe a symbolic framework for treating linear boundary

problems with a generic implementation in the Theorema system. For

ordinary differential equations, the operations implemented include computing

Green’s operators, composing boundary problems and integro-differential

operators, and factoring boundary problems. Based on our

factorization approach, we also present some first steps for symbolically

computing Green’s operators of simple boundary problems for partial

differential equations with constant coefficients. After summarizing the

theoretical background on abstract boundary problems, we outline an

algebraic structure for partial integro-differential operators. Finally, we

describe the implementation in Theorema, which relies on functors for

building up the computational domains, and we illustrate it with some

sample computations including the unbounded wave equation.