| Abstrakt: |
This article establishes an error approximation of a semidiscretized scheme in the solution of a linear partial differential equation initial-valued problem. The error approximation relates the error to both equations and conditions in a problem and serves as a problem-oriented error bound. Two examples of a continuous and a discontinuous wave propagating with a speed varying in space have been studied. The results show that the propagating wave suffers distortion, and the numerical wave is not in synchronization with the exact one. This contributes to that a pointwise error measurement misleads. The discrete Fourier transform can be defined on a finite set of unequally spaced mesh points. Errors of various sources interact and cancel each other; therefore, a solution accuracy improvement can be achieved by utilizing error interaction. |
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