Locally one-dimensional difference scheme for a fractional tracer transport equation

The Crank-Nicholson type compact difference scheme for a loaded time-fractional Hallaire's equation

“…From a priori estimate (18), uniqueness and stability follow, and also the convergence of the solution of the difference problem to the solution of differential problem with the rate O(h 4 + τ 2−α ).…”

“…Various boundary value problems for pseudoparabolic equations were studied in literature [7,8,9,10,11,12,13,14,15,16]. The numerical solutions of the loaded differential equations are discussed by numerous authors [17,18,19,20,21,22,23]. Differential equations of fractional order attract more and more attention of scientists due to the fact that equations of this type can describe many physical and chemical processes, biological environments and systems, which are well interpreted as fractals (i.e soil which is most porous).…”