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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Approximations for weakly nonlinear evolution equations
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by Milan Miklavčič PDF
Math. Comp. 53 (1989), 471-484 Request permission

Abstract:

Convergence of approximations for a large class of weakly nonlinear parabolic and hyperbolic equations is proven. The main emphasis is on proving convergence of finite element and spectral Galerkin approximations of solutions to the weakly nonlinear wave equation \[ u”(t) + Au(t) = F(t,u(t),u’(t)),\quad u(0) = {x_0},u’(0) = {y_0},\] under minimal assumptions on the linear operator A and on the approximation spaces. A can be a very general elliptic operator (not just of 2nd order and not necessarily in a bounded domain); A can also be very singular and degenerate. The results apply also to systems of equations. Verification of the hypotheses is completely elementary for a large class of problems.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 471-484
  • MSC: Primary 65J15; Secondary 65Mxx
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0982370-2
  • MathSciNet review: 982370