A Gaussian quadrature method for the numerical solution of the characteristic intitial value problem 𝑢_{𝑥𝑦}=𝑓(𝑥,𝑦,𝑢)

A Gaussian quadrature method for the numerical solution of the characteristic intitial value problem $u_{xy}=f(x, y, u)$
HTML articles powered by AMS MathViewer

by J. T. Day PDF

Math. Comp. 17 (1963), 438-441 Request permission

References

Preston C. Hammer and Jack W. Hollingsworth, Trapezoidal methods of approximating solutions of differential equations, Math. Tables Aids Comput. 9 (1955), 92–96. MR 72547, DOI 10.1090/S0025-5718-1955-0072547-2
L. Stoller and D. Morrison, A method for the numerical integration of ordinary differential equations, Math. Tables Aids Comput. 12 (1958), 269–272. MR 102180, DOI 10.1090/S0025-5718-1958-0102180-8
Preston C. Hammer and A. Wayne Wymore, Numerical evaluation of multiple integrals. I, Math. Tables Aids Comput. 11 (1957), 59–67. MR 87220, DOI 10.1090/S0025-5718-1957-0087220-6
J. Albrecht and L. Collatz, Zur numerischen Auswertung mehrdimensionaler Integrale, Z. Angew. Math. Mech. 38 (1958), 1–15 (German, with English, French and Russian summaries). MR 93912, DOI 10.1002/zamm.19580380102
Robert H. Moore, A Runge-Kutta procedure for the Goursat Problem in hyperbolic partial differential equations, Arch. Rational Mech. Anal. 7 (1961), 37–63. MR 120772, DOI 10.1007/BF00250749
W. Törnig, Zur numerischen Behandlung von Anfangswertproblemen partieller hyperbolischer Differentialgleichungen zweiter Ordnung in zwei unabhängigen Veränderlichen. I. Das charakteristische Anfangswertproblem, Arch. Rational Mech. Anal. 4 (1960), 428–445 (German). MR 129558, DOI 10.1007/BF00281401

Cours d’Analyse

Wolfgang Walter, Fehlerabschätzungen bei hyperbolischen Differentialgleichungen, Arch. Rational Mech. Anal. 7 (1961), 249–272 (German). MR 125337, DOI 10.1007/BF00250765
Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729