Application of decomposition to convection-diffusion equations
The decomposition method [cf. the author's book: Nonlinear stochastic operator equations (1986; Zbl 0609.60072)] allows a promising approach to a number of significant problems of engineering or physics which are nonlinear and/or stochastic - some formerly intractable, such as Navier- Stokes - with analytic and physically realistic solutions without customary linearization or discretization provided realistic initial- boundary conditions are specified. Application to the nonlinear parabolic partial differential equations \(u_ t-\alpha u_{xx}+f(u,t,x)u_ x\) modeling convection-diffusion processes demonstrates the procedure.
scientific article; zbMATH DE number 4026755