Displaying similar documents to “Simplifying numerical solution of constrained PDE systems through involutive completion”

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

Numerical integration in the Trefftz finite element method

Rozehnalová, Petra

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Using the high order Trefftz finite element method for solving partial differential equation requires numerical integration of oscillating functions. This integration could be performed, instead of classic techniques, also by the Levin method with some modifications. This paper shortly describes both the Trefftz method and the Levin method with its modification.

Verified numerical computations for large-scale linear systems

Katsuhisa Ozaki, Takeshi Terao, Takeshi Ogita, Takahiro Katagiri (2021)

Applications of Mathematics

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This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical...