Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
|Number of page(s)||19|
|Published online||16 April 2019|
On accuracy of numerical solution to boundary value problems on infinite domains with slow decay
Department of Mathematics and Statistics, Thompson Rivers University,
British Columbia, Canada.
* Corresponding author: email@example.com
Accepted: 28 January 2019
A numerical approach is developed to solve differential equations on an infinite domain, when the solution is known to possess a slowly decaying tail. An unorthodox boundary condition relying on the existence of an asymptotic relation for |y| ≫ 1 is implemented, followed by an optimisation procedure, allowing to obtain an accurate solution over a truncated finite domain. The method is applied to −(−Δ)γ/2u − u + up = 0 in ℝ, a non-linear integro-differential equation containing the fractional Laplacian, and is easily expanded to asymmetric boundary conditions or domains of a higher dimension.
Mathematics Subject Classification: 45K05 / 37M99
Key words: Slowly decaying tail / infinite domain / boundary value problem / fractional Laplacian / ground state solution
© EDP Sciences, 2019
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