Abstract
In partial differential equations (PDEs), the unknown function is dependent on more than one independent variable. While many linear PDEs can be solved analytically, the nonlinear PDEs may not be amenable to analytical solutions. Also, the computational challenge may become rather demanding when solving nonlinear PDEs. Second-order linear PDEs can be classified as parabolic, hyperbolic, and elliptic which may describe a diffusion process, wave propagation, and steady-state (time independent) phenomena, respectively. This chapter presents either implicit or explicit solutions to the following linear parabolic, hyperbolic, and elliptic equations and nonlinear elliptic equations:
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Madenci, E., Barut, A., Dorduncu, M. (2019). Partial Differential Equations. In: Peridynamic Differential Operator for Numerical Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-02647-9_6
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DOI: https://doi.org/10.1007/978-3-030-02647-9_6
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