in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and nonlinear memory source term. For 1, will be considered on bounded domain ℝ d . By some Sobolev embeddings properties Mittag-Leffler function, give results existence uniqueness mild solution (1.1) below. When = introduce L p −...

Abstract We consider a one-Laplace equation perturbed by p -Laplacian with $$1<p<\infty $$ 1 < p ∞ . prove that weak solution is continuously differentiable $$(C^1)$$ ( C ...

We present an adaptive animation method for electrical discharges. Electric discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discret...

<p style='text-indent:20px;'>We study the inverse problem for fractional Laplace equation with multiple nonlinear lower order terms. We show that direct is well-posed and uniquely solvable. More specifically, unknown nonlinearities can be determined from exterior measurements under suitable settings.</p>