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Pure InitialValue Problems with Constant Coefficients
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accuracy amplification appear applied approximation assume Banach space boundary conditions bounded calculation called Chapter characteristic coefficients components consider consistency constant continuous convergence corresponding curve defined denote depends derivatives described determined difference equations difference scheme differential equations discussed effect eigenvalues elements energy equal equivalent error example exists expression fact factor Figure finite finite-difference fixed fluid follows formula Fourier function further given gives hence implicit inequality initial initial-value problem integral interval limit linear matrix mesh method necessary Neumann norm normal obtained operator posed positive practical present procedure properly prove quantities replaced restriction result satisfied sequence shock shown similar simple smooth solution solved space speed stability stability condition sufficient suppose surface taken theorem tion transformation unit values variable vector von Neumann wave zero