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Solution of 1D Wave Equation in Polar Coordinates using
Cubic B-Spline Quasi Interpolation
Muhammad Faqihul Ajmal Bin Hakimin
Supervisor: Dr. Fatimah Noor Binti Harun
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
In this research, the cubic B-splines Quasi Interpolation method is considered for solving
one dimensional wave equation in polar coordinates. This research was conducted to
solve 1 dimensional wave equation in polar coordinates using cubic B-spline Quasi
Interpolation and compare the results of numerical experiments with analytical solutions.
A typical forward difference approach had been used to discretize the time derivative
while the cubic B-spline Quasi Interpolation is applied as an interpolation function in the
spatial derivative where these two methods are applied to singular hyperbolic equation.
The accuracy of the method for both equations is discussed. The efficiency of the method
is illustrated by some test problems. The results of numerical experiments are compared
with analytical solutions by calculating root-mean-square error L 2 and maximum error
L ∞ . From the test examples, we can say that the B-spline Quasi Interpolation scheme is
feasible and the error is acceptable.
950 | UMT UNDERGRADUATE RESEARCH DAY 2018