NUMERICAL SOLUTION OF HYPERBOLIC GOURSAT PARTIAL DIFFERENTIAL EQUATIONS WITH HYBRID CENTRAL DIFFERENCE - TAYLOR SERIES EXPANSIONS METHOD
Ros Fadilah Deraman1*, Mohd Agos Salim Nasir2, Rizauddin Saian3
1*College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Cawangan Negeri Sembilan, Kampus Kuala Pilah, 72500 Kula Pilah, Malaysia
2College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Cawangan Selangor, Kampus Shah Alam, 40450 Shah Alam, Malaysia
3College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Cawangan Perlis, Kampus Arau, 02600 Arau, Malaysia
1*This email address is being protected from spambots. You need JavaScript enabled to view it., 2This email address is being protected from spambots. You need JavaScript enabled to view it., 3This email address is being protected from spambots. You need JavaScript enabled to view it.
ABSTRACT
This paper investigates a new method for solving the Goursat partial differential equation (PDE) using a combination of the central finite difference method (FDM) and Taylor series expansion. The study evaluates the effectiveness and accuracy of this new approach, analyzing linear Goursat problems and conducting multiple numerical experiments. The simulation study demonstrates that the suggested approach surpasses the existing method in terms of performance and accuracy. Applying this proposed scheme will minimize the cost, especially for engineers that might apply this model in solving their real-life problems.
Keywords: Central Finite Difference Method, Goursat Problem, Hyperbolic Partial Differential Equation, Numerical Differentiation, Taylor Series Expansions
Published On: 1 April 2024
