, Volume 7, Issue 1–2, pp 13–16 | Cite as

On the numerical solution of a certain class of non-linear cauchy problems arising from integral equation theory

  • Richard C. AllenJr.


A numerical algorithm for solving a system of non-linear partial differential integral equations is presented. These equations result from applying the method of invariant imbedding to the solution of a certain class ofFredholm integral equations of the second kind [2]. The algorithm is compared with a more standard method of solution and some numerical results presented.


Integral Equation Numerical Algorithm Computational Algorithm Quadrature Formula Actual Answer 


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  1. [1]
    Chandrasekhar: Radiative Transfer. New York: Dover Publications Inc. 1960.MATHGoogle Scholar
  2. [2]
    Wing, G. M.: On CertainFredholm Integral Equations Reducible to Initial Value Problems. SIAM Review9, 655–670 (1967).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Richard C. AllenJr.
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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