This analysis derives solutions for partial differential equations with modifications, indicating a new method for complex equations.
This paper presents analytical solutions for third-order partial differential equations with integer-order derivatives derived using a third-order formulation with constant coefficients. The study provides analytical expressions that satisfy these partial differential equations by applying the modified double Laplace decomposition method under specific initial and boundary conditions. Then we found the error values and figured them out using the MATLprogram.
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Abdulla et al. (2025) studied this question.
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