Semi-analytical solution of physical initial-value problemsusing the imprint method

Abstract: Numerical solution of partial differential equations is often restricted toinclude parametrical dependence through a series of calculations. The imprintmethod, which is a semi-analytical spectral method taking advantage of todayspowerful symbolic computer mathematics, include parametrical dependence byallowing an arbitrary number of variables and parameters within the solution.In this Master's thesis the imprint method is evaluated for both polynomialand Chebyshev basis functions. Benchmarking is done mainly against theBurgers equation, which allows comparisons with exact solutions.Much of this thesis work is also dedicated to produce a versatileimplementation for the Maple platform.