id: 06439626
dt: j
an: 2015d.00951
au: Tay, Kim Gaik; Kek, Sie Long; Abdul-Kahar, Rosmila
ti: A spreadsheet solution of a system of ordinary differential equations using
the fourth-order Runge-Kutta method.
so: Spreadsheets Educ. 5, No. 2, 10 p., electronic only (2012).
py: 2012
pu: Bond University, Faculty of Business, Gold Coast, Queensland
la: EN
cc: N45 I75 M55 U75
ut: systems of ordinary differential equations; spreadsheets; fourth-order
Runge-Kutta methods; numerical examples; electrodynamics; teaching;
computer as educational medium; calculators
ci:
li: http://epublications.bond.edu.au/ejsie/vol5/iss2/5/
ab: Summary: Solving systems of ordinary differential equations (ODEs) by using
the fourth-order Runge-Kutta (RK4) method in classroom or in
examinations is quite tedious, tiring and boring since it involves many
iterative calculations. Hence, there is a need to design a suitable
tool in teaching and learning the numerical methods involved,
especially those for solving systems of ODEs. Here, we present a new
approach to solving systems of ODEs by the RK4 method through the use
of an Excel spreadsheet to tackle these drawbacks. In doing so, we
employ the concept of relative row, relative column and fixed column in
the spreadsheet to obtain the solution of systems of ODEs by the RK4
method. With the appropriate differential function given by the user,
it is found that the way suggested here is faster than applying a
scientific calculator and the solution obtained is significantly more
accurate. Besides, the concept presented here can be extended to solve
systems of ODEs up to $n$ equations using the spreadsheet. In addition
to this, the students can gain a deep understanding of the iterative
procedure involved in solving the systems of ODEs. Although the
spreadsheet approach is not as good as other mathematical software, it
does provide a step-by-step environment for teaching and learning the
numerical methods. We conclude that the spreadsheet approach increases
the interest of students in learning the RK4 method.
rv: