Polynomially bounded error estimates for Trapezoidal Rule Convolution Quadrature
نویسندگان
چکیده
منابع مشابه
Notes on the convergence of trapezoidal - rule quadrature
Numerical quadrature is another name for numerical integration, which refers to the approximation of an integral ́ f (x)dx of some function f (x) by a discrete summation ∑wi f (xi) over points xi with some weights wi. There are many methods of numerical quadrature corresponding to different choices of points xi and weights wi, from Euler integration to sophisticated methods such as Gaussian quad...
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and |g′′(x)| = M. We will show that |f(x)| ≤ g(x) on [0, 1]. The desired conclusion follows. Suppose however that this is false, that there is a number q ∈ [0, 1] for which f(q) > g(q). (The other case, f(q) < −g(q), is similar.) Our strategy will be to show that there are real numbers s and t with s < t such that f ′(s) > g′(s) and f ′(t) < g′(t). See figure. We will then apply the Mean Value ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2020
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2019.09.020