Authors :
Parth Singh Pawar; Dhananjay R. Mishra; Pankaj Dumka
Volume/Issue :
Volume 7 - 2022, Issue 3 - March
Google Scholar :
https://bit.ly/3IIfn9N
Scribd :
https://bit.ly/37oG4mE
DOI :
https://doi.org/10.5281/zenodo.6418458
Abstract :
In this research article an attempt has been
made to examine the performance of Finite difference
method (FDM) and Least square method (LSM) on the
solution of first order ordinary differential equations
(ODE). Both FDM and LSM are applied on the test
problem and the results thus obtained are compared with
the exact solution. It has been observed that for third
degree basis function the results of LSM very close to the
analytical result. On further increasing the degree the
improvement in the result is very meagre and N=3 can be
considered as the optimum solution for LSM. It has also
been observed that the FDM is very sensitive to the
number of grid points and deviates from the exact results
by a substantive amount for lower number of nodes.
Whereas the LSM is independent of the number of nodes.
Keywords :
Least Square Method; Finite Difference Method; Ordinary Differential Equation; Python; Optimization.
In this research article an attempt has been
made to examine the performance of Finite difference
method (FDM) and Least square method (LSM) on the
solution of first order ordinary differential equations
(ODE). Both FDM and LSM are applied on the test
problem and the results thus obtained are compared with
the exact solution. It has been observed that for third
degree basis function the results of LSM very close to the
analytical result. On further increasing the degree the
improvement in the result is very meagre and N=3 can be
considered as the optimum solution for LSM. It has also
been observed that the FDM is very sensitive to the
number of grid points and deviates from the exact results
by a substantive amount for lower number of nodes.
Whereas the LSM is independent of the number of nodes.
Keywords :
Least Square Method; Finite Difference Method; Ordinary Differential Equation; Python; Optimization.
