Collocation and residual correction
Tóm tắt
After applying the collocation method with piecewise polynomial functions, on linear two-point-boundary-value ordinary differential equations, we correct the approximated solution using the residual function of the operator equation. That residual function will be the second member of the error differential equation. Solving this by some accurate finite-difference method, say of orderp, we correct the collocation approximation getting a new one which is of orderp too.
Tài liệu tham khảo
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Frank, R., Ueberhuber, C.W.: Collocation and iterated defect correction. Lectures Notes in Mathematics Vol. 631. Berlin Heidelberg New York: Springer 1976
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Prenter, P.M.: Splines and variational methods, New York: Wiley 1975
Russell, R.D., Shampine, L.F.: A collocation method for boundary value problems. Numer. Math.19, 1–28 (1972)
Weiss, R.: The application of implicit Runge-Kutta and collocation methods to boundary value problems. Math. Comput.28, 449–464 (1974)