Abstract
A procedure, using spline functions of degreem, deficiencyk − 1, for obtaining approximate solutions to nonlinear Volterra integral equations of the second kind is presented. The paper is an investigation of the numerical stability of the procedure for various values ofm andk.
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References
J. H. Ahlberg, et al,The Theory of Splines and Their Applications, Academic Press, 1967.
G. Dahlquist,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43.
M. E. A. El Tom,Application of spline functions to Volterra integral equations, J. Inst. Maths. Applics 8, (1971), 354–357.
M. E. A. El Tom,Numerical solution of Volterra integral equations by spline functions, BIT 13 (1973), 1–7.
B. Noble,Applied Linear Algebra, Prentice Hall, 1966.
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El Tom, M.E.A. On the numerical stability of spline function approximations to solutions of Volterra integral equations of the second kind. BIT 14, 136–143 (1974). https://doi.org/10.1007/BF01932942
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DOI: https://doi.org/10.1007/BF01932942