Projected collocation for higher-order higher-index differential- algebraic equations
The authors extend some of their previous results [SIAM J. Numer. Anal. 28, No. 4, 1097-1120 (1991; Zbl 0732.65067)] to differential-algebraic equations of the type \(x^{(m)} = f(x^{(m-1)},\dots,\) \(x',x,y,t)\), \(0 = g(x,t)\), where \(x(t) \in \mathbb{R}^ n\), together with a set of boundary conditions. Main attention is paid to the linear case \(f(z_ m,\dots,z_ 1,y,t) = \sum^ m_{j=1}A_ j(t)z_ j + B(t)y + q(t)\), \(g(x,t) = C(t)x + r(t)\). A projection collocation scheme is discussed which yields a stable superconvergent integration method. Numerical examples are considered comparing the Gauss and Radau collocation schemes.
scientific article; zbMATH DE number 85933
scientific article