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- W182738505 abstract "This chapter focuses on extrapolation processes and singularities. The concept of extrapolation has played a significant role in numerical mathematics. It can be exploited to obtain a numerical estimate for the physical constant π by observing that the perimeter of a regular n -sided polygon inscribed in a circle with unit diameter is given as s ( n ) = n sin π/ n and that this can be made to be as close as possible to the circumference of the circle by choosing n sufficiently large. The main concern is to make use of this versatile and important tool called extrapolation to increase the order of the numerical results generated by the lower order discretization schemes for the initial value problem (IVP) without seriously jeopardizing the stability properties of the original method. The chapter presents an observation in which it was observed that the trapezoidal rule is more accurate and possesses better stability properties than Euler's scheme. Besides, the trapezoidal scheme possesses an error expansion in even powers of h provided it is implemented in the iteration to convergence mode." @default.
- W182738505 created "2016-06-24" @default.
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- W182738505 date "1988-01-01" @default.
- W182738505 modified "2023-09-26" @default.
- W182738505 title "EXTRAPOLATION PROCESSES AND SINGULARITIES" @default.
- W182738505 doi "https://doi.org/10.1016/b978-0-12-249930-2.50011-4" @default.
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