Numerical Solution: A Study of Partially Differential Equation
Keywords:
Partial differential equations, Numerical methods, SolutionAbstract
This study explores various numerical methods for solving partial differential equations (PDEs), which are crucial in modeling complex phenomena across diverse scientific and engineering fields. Given the challenges associated with obtaining analytical solutions for PDEs, numerical approaches such as the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM) have become essential. This research provides a comparative analysis of these techniques, evaluating them based on accuracy, computational efficiency, and applicability to different types of PDEs, including elliptic, parabolic, and hyperbolic equations. Through a series of test cases, the study highlights the strengths and weaknesses of each method, offering practical insights into their use for solving PDEs in real-world scenarios.
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