NDSolve has a facility for users and package developers to add their own methods. After demonstrating the template required for basic method construction, more advanced ...

This item contains numerical analysis software coded in Mathematica 5.2. The examples are described in the text "Numerical Methods," 4th Edition, 2006. See item 2999 for ...

In this note, an improvement to the code from an earlier article on the shooting method is presented.

A four lecture undergraduate engineering course on variational methods and stress analysis. Lecture 1: Fundamentals of elasticity: strain energy density, generalised Hooke's ...

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse ...

In this paper, we study a new coupled system (KdV6) from the point of view of constructing exact solutions for it by using the Cole–Hopf transformation and one improved ...

It would seem that limiting computer computations to numbers with a fixed number of decimal digits would inhibit flexibility. Software programs such as Mathematica permit ...

In the present notebook, the author has found a new way to solve split boundary value problems using the shooting technique. The new approach is based on NDSolve`StateData ...

Decision tree models may be more realistic if branching probabilities (and possibly utilities) are represented as distributions rather than point estimates. However, ...

Modified Runge–Kutta (mRK) methods can have interesting properties as their coefficients may depend on the step length. By a simple perturbation of very few coefficients we ...