Introducing Monte Carlo Methods with R Solutions to Odd-Numbered Exercises

This is the solution manual to the odd-numbered exercises in our book "Introducing Monte Carlo Methods with R", published by Springer Verlag on December 10, 2009, and made freely available to everyone.Comment: 87 pages, 11 figure

Stability regions of numerical methods for solving fractional differential equations

This dissertation deals with proper consideration of stability regions of well known numerical methods for solving fractional differential equations. It is based on the algorithm by Diethelm [15], predictor-corrector algorithm by Garrappa [31] and the convolution quadrature proposed by Lubich [3]. Initially, we considered the stability regions of numerical methods for solving ordinary differential equation using boundary locus method as a stepping stone of understanding the subject matter in Chapter 4. We extend the idea to the fractional differential equation in the following chapter and conclude that each stability regions of the numerical methods differs because of their differences in weights. They are illustrated by a number of graphs