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| A Novel Approach to Solving Third-Order PDEs Using the Adomian Decomposition Method |
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| KeyWord:KdV equation, third-order PDEs, ADM, Adomian polynomials, boundary value problem |
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| Abstract: |
| This study investigates the solution of third-order partial differential equations (PDEs), a class of equations that model a wide range of physical phenomena. The focus is on the Korteweg-de Vries (KdV) equation, a fundamental model for nonlinear wave propagation. To achieve the study's objectives, the Adomian decomposition method (ADM) is employed as an analytical tool to solve this equation. This method is well-known for its capability to handle nonlinear equations and provide highly accurate analytical solutions. By applying this method, exact solutions to the equation were obtained, as illustrated in the presented examples. These exact solutions demonstrate the effectiveness and power of the proposed method in dealing with this type of equation. The obtained results confirm that the ADM is a robust and reliable tool for solving nonlinear partial differential equations, opening new avenues for its application in various scientific and engineering fields. |
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