Collocation for singular boundary value problems of second order

The collocation methods for solving linear boundary value problems with a singularity of the first kind are investigated. The stability and convergence results are established. Particular attention is paid to the superconvergence properties of the methods, which are different as in the classical case when the singularity is not present. The results are extended to the nonlinear case and illustrated by numerical examples.

[1]  Ewa Weinmüller,et al.  On the Boundary Value Problem for Systems of Ordinary Second Order Differential Equations with a Singularity of the First Kind , 1984 .

[2]  M. Abramowitz,et al.  Mathematical functions and their approximations , 1975 .

[3]  Robert D. Russell,et al.  Collocation for systems of boundary value problems , 1974 .

[4]  A generalized spline method for singular boundary value problems of ordinary differential equations , 1973 .

[5]  H. B. Keller,et al.  A NUMERICAL METHOD FOR SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS , 1977 .

[6]  Seymour V. Parter,et al.  On the Multiplicity of Solutions Of a Differential Equation Arising in Chemical Reactor Theory , 1975 .

[7]  F. Hoog,et al.  Collocation Methods for Singular Boundary Value Problems , 1978 .

[8]  L. Shampine,et al.  A collocation method for boundary value problems , 1972 .

[9]  C. D. Boor,et al.  Package for calculating B-splines , 1977 .

[10]  C. D. Boor,et al.  Collocation at Gaussian Points , 1973 .

[11]  Edward L. Reiss,et al.  Axisymmetric buckling of hollow spheres and hemispheres , 1970 .

[12]  Richard Weiss,et al.  The application of implicit Runge-Kutta and collection methods to boundary-value problems , 1974 .

[13]  Pierre Jamet.  On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems , 1970 .

[14]  H. Keller,et al.  Approximation methods for nonlinear problems with application to two-point boundary value problems , 1975 .

[15]  Seymour V. Parter.  A POSTERIORI ERROR ESTIMATES , 1975 .

[16]  H. Keller,et al.  On the Nonunique Equilibrium States and Buckling Mechanism of Spherical Shells , 1965 .

[17]  U. Ascher,et al.  A collocation solver for mixed order systems of boundary value problems , 1979 .