This article presents two methods for computing interval bounds on the solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). Part 1 presents theoretical developments, while Part 2 discusses implementation and numerical examples. The primary theoretical contributions are (1) an interval inclusion test for existence and uniqueness of a solution, and (2) suffici...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

Richardson splitting applied to a consistent system of linear equations Cx = b with a singular matrix C yieJds to an iterative method ..1+1 = Axk + b where A has the eigenvalue one. It is known that each sequence of iterates is convergent to a vector x* = x*(xO)if and onJy if A is semi-convergent. In order to enclose such vectors we consider the corresponding interval iteration [X]k+1 = [A][x]k...

For the linear regression model , we consider the problem of data fitting under interval uncertainty. Let an interval × -matrix = ( ) and an interval -vector = ( ) represent the input data and output responses of the model respectively, such that , , ... , , in the -th experiment, = 1, 2, ... , . It is necessary to find the coefficients that best fit the above linear relation for the data given...

one-third of the people with an age over twenty have some signs of degenerated discs. however, in most of the patients the mere presence of degenerative discs is not a problem leading to pain, neurological compression, or other symptoms. this paper presents an interval type-2 fuzzy hybrid rule-based system to diagnose the abnormal degenerated discs where pain variables are represented by interv...