DOUBLE INTEGRATION USING CUBIC SPLINES

Williams, R (1983). DOUBLE INTEGRATION USING CUBIC SPLINES. BPhil thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f7e3

Abstract

This dissertation applies the approximation methods of the cubic spline and the bicubic spline to the problem of integration in two dimensions. The dissertation is divided into six sections.
Section 1 is the Introduction and contains background material concerning the historical introduction and theory of the cubic spline together with a resume of what i t is intended to achieve in the body of the dissertation.
Section, 2 contains a description of the derivation of the tradit­ional algorithm for computing a one dimensional cubic spline approximation to a function f(x) and then we integrate this cubic spline to find an approximation to the integral of f(x).
In Section 3 we express the integral of a function f(x) as a function of its upper limit and then fit a one dimensional cubic spline to this integral directly.
In Section 4 we apply the methods of Sections 2 and 3 to evaluate integral approximations to functions of two variables.
In Section 5 we fit a Bicubic Spline to the mesh values of a function of two variables over a rectangular mesh and integrate this bicubic spline approximation to give an approximate value of the double integral of the function.
Section 6 contains the conclusions drawn from the proceeding computations

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