A compact ADI scheme for the two dimensional time fractional diffusion‐wave equation in polar coordinates. Issue 5 (28th March 2015)

• Record Type: Journal Article
• Authors: Vong, Seakweng; Wang, Zhibo
• Is Part Of: Numerical methods for partial differential equations. Volume 31:Issue 5(2015)
• Page Start: 1692
• Page End: 1712
• Publication Date: 2015-03-28
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21976
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this article, we consider finite difference schemes for two dimensional time fractional diffusion‐wave equations on an annular domain. The problem is formulated in polar coordinates and, therefore, has variable coefficients. A compact alternating direction implicit scheme with <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj25zbwfg8" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:0749159X:media:num21976:num21976-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mo>τ</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mo>α</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>h</mml:mi><mml:mn>1</mml:mn><mml:mn>4</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>h</mml:mi><mml:mn>2</mml:mn><mml:mn>4</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> accuracy order is derived, where <italic>τ, h</italic><sub>1</sub>, <italic>h</italic><sub>2</sub> are the temporal and spatial step sizes, respectively. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. Numerical experiments are presented to support the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1692–1712, 2015</p> </abstract>