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A Runge-Kutta procedure for the goursat problem in hyperbolic partial differential equations

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References

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    Diaz, J. B.: On an analogue of the Euler-Cauchy polygon method for the numerical solution of ux,y=f(x,y,u,ux,uy). Arch. Rational Mech. Anal. 1, 357–390 (1958).

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    Kutta, W.: Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Z. Math. Phys. 46, 435–453 (1901).

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    Moore, R. H.: On approximate solutions of non-linear hyperbolic partial differential equations. Arch. Rational Mech. Anal. 6, 75–88 (1960).

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    Prasad, G.: Six Lectures on Mean Value Theorems of Differential Calculus. Univ. of Calcutta, 1931.

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    Runge, C.: Über die Numerische Auflösung von Differentialgleichungen. Math. Ann. 46, 167–178 (1895).

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Communicated by L. Cesari

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Moore, R.H. A Runge-Kutta procedure for the goursat problem in hyperbolic partial differential equations. Arch. Rational Mech. Anal. 7, 37–63 (1961). https://doi.org/10.1007/BF00250749

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Keywords

  • Partial Differential Equation
  • Taylor Expansion
  • Taylor Series Expansion
  • Regularity Assumption
  • Convergence Proof