Analytical solution methods for boundary value problems. Translated from the Russian (Q2823267)

In the present book analytical solution methods for nonlinear boun\-dary value problems are developed. The method of quasi-linearization, operational calculation and locally one-dimensional schemes are used. Estimations of the speed of convergence of the iterative processes are also investigated. NEWLINENEWLINENEWLINEThe book consists of 5 chapters. In Chapter 1 technology for solution of the tree-dimensional linear transfer equation \(u_t+\sum_{m=1}^3c_mu_{x_m}=f(t,x)\), \(u\geq0\) on the basis of operational calculation is worked out. Analytical formulas for the solution of the tree-dimensional elliptic equation with constant coefficients \(\sum_{m=1}^3(A_m T_{x_mx_m}+ B_mT_{x_m})+CT+f(x)=0\) in a parallelepiped are also obtained. In Chapter 2 solvability of one-dimensional and tree-dimensional nonlinear transfer equations \(A_4u_t+\sum_{j=1}^3A_j(uw(u))_{x_j}=E(u,x,t)\), \(u\geq0\) are investigated, and estimation of the speed of convergence of the iterative process is given. In Chapter 3 for nonlinear one-dimensional and tree-dimensional first boundary value problems for parabolic equation the estimation of rate of convergence of the iterative process is found. Method of solution of conjugate boundary value problems is presented in Chapter 4: conjugate problems of heat-exchange and approximate analytical solutions of nonlinear problems in one-dimensional and tree-dimensional cases are given. In Chapter 5 methods of solution of one-dimensional and tree-dimensional telegraph equations are discussed.