Solving Fredholm Integral Equations Using Chebyshev Polynomials

Abstract

In this thesis, we study the approximation of the Fredholm integral equation of the second kind using Chebyshev series expansions. We also modified the resulting algorithms to be suitable for running on a Graphics Processing Unit (GPU). With fixed precision, the results of this method become inaccurate due to the exponential growth of the matrix condition number as number of terms in the series increases. The GPU implementation of the modified algorithm attained a significant speedup compared to the Central Processing Unit (CPU). However, the GPU libraries currently support neither an adaptive step size for integration nor arbitrary precision and therefore experienced larger error than the CPU implementation.