A Python Implementation of Explicit 2step Methods
(2015) In Bachelor's Theses in Mathematical Sciences NUMK01 20151Mathematics (Faculty of Technology) and Numerical Analysis
 Abstract
 This paper shows the Python implementation of a new way of constructing a variable multistep ODE solver which is not based on extending fixed stepsize methods but rather on defining interpolation and collocation conditions for each new point. The implementation allows for any explicit 2step method of order 2.
 Popular Abstract
 Companies often want to solve different kinds of problems that require numerical solutions. Some of those problems can be modeled with ordinary differential equations. Often, to solve these problems, the calculations are long and very hard, so they need special methods and the use of computers. That is why there exist numerical methods so that the computer can solve the equation for you. One special kind of differential equation is called the initial value problem. This paper will be about converting a code for solving initial value problems from a language called Matlab into another program language called Python.
Since Matlab is a paid source and Python is an open source, which means that everybody can use it, converting this code... (More)  Companies often want to solve different kinds of problems that require numerical solutions. Some of those problems can be modeled with ordinary differential equations. Often, to solve these problems, the calculations are long and very hard, so they need special methods and the use of computers. That is why there exist numerical methods so that the computer can solve the equation for you. One special kind of differential equation is called the initial value problem. This paper will be about converting a code for solving initial value problems from a language called Matlab into another program language called Python.
Since Matlab is a paid source and Python is an open source, which means that everybody can use it, converting this code into Python will result in a larger exposure of the method. The code constructs piecewise polynomials of degree 2 in order to solve the initial value problem. This is a novel technique that has not been used before.
By just changing one parameter in the code all variable stepsize explicit methods of order 2 for solving initial value problems can be obtained. This paper also shows which methods are stable and runs different tests to check if the code is working properly. In the end we have implemented a new numerical way of solving the initial value problem. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/7356736
 author
 Persson, Kevin ^{LU}
 supervisor

 Carmen ArĂ©valo ^{LU}
 Fatemeh Mohammadi ^{LU}
 organization
 course
 NUMK01 20151
 year
 2015
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFNA40042015
 ISSN
 16546229
 other publication id
 2015:K6
 language
 English
 id
 7356736
 date added to LUP
 20160825 15:39:32
 date last changed
 20160825 15:39:32
@misc{7356736, abstract = {This paper shows the Python implementation of a new way of constructing a variable multistep ODE solver which is not based on extending fixed stepsize methods but rather on defining interpolation and collocation conditions for each new point. The implementation allows for any explicit 2step method of order 2.}, author = {Persson, Kevin}, issn = {16546229}, language = {eng}, note = {Student Paper}, series = {Bachelor's Theses in Mathematical Sciences}, title = {A Python Implementation of Explicit 2step Methods}, year = {2015}, }