INTEGRAL, AND INFINITE CONSTRAINTS LINEAR DIFFERENTIAL EQUATIONS SUBJECT TO RELATIVE

2018 Univelt Inc. All rights reserved. This study extends prior work in the Theory of Connections (ToC) by detailing methods to incorporate relative, integral, and infinite constraints. In this, the method produces analytical constrained expressions that always satisfy the given constraints while remaining free in the function g(x). For some cases, numerical tests were conducted where least-squares solutions are obtained for ordinary differential equations by using a two step process. First, the constrained expression is derived and the free function, g(x), is then expanded as a linear combination of a set of basis functions (e.g., nonrational and rational orthogonal polynomials). In the second step, the unknown coefficients of this expansion are estimated by least-squares using collocation point discretization. The results obtained by the proposed method are then compared in terms of speed and accuracy with the solution provided by the Chebfun toolbox. In all numerical examples, the proposed method produces a solution more accurate and with two orders of magnitude faster solution time compared to Chebfun.

LINEAR DIFFERENTIAL EQUATIONS SUBJECT TO RELATIVE, INTEGRAL, AND INFINITE CONSTRAINTS Conference Paper