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Blog Archives
Nakao’s method and an interval difference scheme of second order for solving the elliptic BVP
In the paper we compare Nakao’s method to our interval difference scheme of second order. Repeating some computational examples of Nakao, we have observed that our implementation of his method gives better results. Moreover, it appears that the presented interval difference scheme gives better ...
Interval Runge-Kutta Methods with Variable Step Sizes
In a number of our previous papers we have presented interval versions of Runge-Kutta methods (explicit and implicit) in which the step size was constant. Such an approach has required to choose manually the step size in order to ensure an interval enclosure to the solution with the smallest widt ...
On Two Families of Implicit Interval Methods of Adams-Moulton Type
In our previous paper [1] we have presented implicit interval methods of Adams-Moulton type. It appears that two families of these types of methods exist. We compare both families of methods and present a numerical example.
Multistep Interval Methods of Nyström and Milne-Simpson Types
The paper is dealt with two kinds of multistep intervals methods which can be used to solve the initial value problem in the form of intervals containing all possible numerical errors. The interval methods of Nyström type are explicit, while the methods of Milne- Simpson are implicit. It appears ...