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New results on the approximation of solutions to partial differential equations: The method of particular solutions

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Book cover Analytic Theory of Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 183))

This research has been supported in part by the Air Force Office of Scientific Research through AFOSR-Grant 1206-67.

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References

  1. D. Colton and R.P. Gilbert, Cauchy's problem for elliptic equations in several independent variables, to appear.

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  2. N. Du Plessis, Runge's theorem for harmonic functions, J. London Math. Soc. (2) 1 (1969), 404–408.

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  3. P.R. Garabedian, Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech. 9 (1960), 241–271

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  4. R.P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.

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  5. R.P. Gilbert and C.Y. Lo, On the approximation of solutions of elliptic partial differential equations in two and three dimensions, to appear.

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  6. B.L. Tjong, Operators generating solutions of Δ3ψ(x,y,z)+F(x,y,z)ψ(x,y,z)=0 and their properties, in Analytic Methods in Mathematical Physics, edited by R.P. Gilbert and R.G. Newton, Gordon and Breach, New York, 1970.

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  7. D.V. Widder, Expansions in series of homogeneous polynomial solutions of the two-dimensional wave equation, Duke Math. J. 26 (1959), 591–598.

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Authors and Affiliations

  1. Indiana University, USA

    David Colton & Robert P. Gilbert

Authors
  1. David Colton
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  2. Robert P. Gilbert
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P. F. Hsieh A. W. J. Stoddart

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© 1971 Springer-Verlag

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Colton, D., Gilbert, R.P. (1971). New results on the approximation of solutions to partial differential equations: The method of particular solutions. In: Hsieh, P.F., Stoddart, A.W.J. (eds) Analytic Theory of Differential Equations. Lecture Notes in Mathematics, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060421

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  • DOI: https://doi.org/10.1007/BFb0060421

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05369-9

  • Online ISBN: 978-3-540-36454-2

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