Numerical Solution of Two-dimensional and Three-dimensional Boundary-value Problems of Mathematical Physics

Nonclassical mathematical model in geoinformatics to solve dynamic problems for nonequilibrium nonisothermal seepage fields

“…Passing to dimensionless variables in (12)- (14) and (18)- (20) according to (21) and omitting the prime over the dimensionless quantities, we obtain the following nonlinear boundary-value problem:…”

Mathematical modeling of filtration consolidation with salt transfer in a double-relaxation system

“…Passing to original functions in (24), we get the solution of the original differential-difference problem as In view of the aforesaid, we can propose a technique to solve the boundary-value problem (9)- (14), based on the joint application of the differential-difference and difference methods, the concentration field being calculated according, for example, to the difference scheme written in the notation from [16] as…”

“…Let us first consider the problem (9), (11), (12) with the function C assumed known and apply the approach proposed in [13], which combines the differential-difference method and the method of aggregate representations [14]. To this end, we introduce a mesh domain …”

Mathematical modeling of the dynamics of consolidation processes with relaxation effects

“…First, let us consider the problem (2), (4)-(6) for the excess head and apply the differential-difference method combined with the method of total representations [10,11]. To this end, let us introduce a mesh domain…”