Abstract
A lot of software today dealing with various domains of engineering and life sciences have to deal with non-linear problems. In order to reduce the problem to a linear problem, a lot of state of the art solutions already exist. This work focus on the implementation of Newton’s Algorithm (also known as Newton’s method), to determine the roots of a given function within a specific user defined interval. The software for this implementation is FORTRAN. Even though FORTRAN is considered to be outdated, it still has a lot of application due to its long history and the existing legacy code. The code is written in such a manner that a user can provide a function and a specific interval and the code should in turn run iterations over the interval and should display all the possible roots within that interval. The results are compared at the end for their accuracy. The program is successful in finding out all the roots within an interval.
Highlights
FORTRAN programming language has been one of the earliest of its kind to be in use for the purpose of writing programs
In that regard, learning it is necessary to have a better grasp on it, in order to have a better understanding of those programming languages that followed
It was asked to make a program on FORTRAN, that uses Newton’s method as its base to approximate the roots of a function over a fixed interval
Summary
FORTRAN programming language has been one of the earliest of its kind to be in use for the purpose of writing programs. It was asked to make a program on FORTRAN, that uses Newton’s method as its base to approximate the roots of a function over a fixed interval (both the function and the interval are to be given by the user). We examine three variations of the strategy initiating from Newton’s strategy for discovering the roots of a function of a sole variable: the method in higher dimensions, higher order method, and continuous method. Imperative hypothetical outcomes on Newton’s method regarding the convergence properties, the error estimates, the numerical stability and the computational complexity of the algorithm were assessed. The first one, for finding roots of scalar functions, is the numerical comparison between the new Newton formulas, Newton’s method and a third order Newton method. We observe that the offered algorithm is effective for one dimensional real function [3]
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