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Laplace transform and homotopy perturbation methods for solving the pseudohyperbolic integrodifferential problems with purely integral conditions. (English) Zbl 1494.35121

Summary: In this paper we defined and investigated the various properties of a class of pseudohyperbolic equation defined on purely integral (nonlocal) conditions. We proved the uniqueness and the existence of the solution using energy inequality (A priori estimates). We found a semi analytical solution using the Laplace transform and Stehfest algorithm method. Next, we used another method called the Homotopy perturbation. Finally, we give some examples for illustration.

MSC:

35L82 Pseudohyperbolic equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35R09 Integro-partial differential equations
44A10 Laplace transform
45J05 Integro-ordinary differential equations
65R20 Numerical methods for integral equations
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References:

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