Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation

“…A triple ( * , u * [t], * ) with elements * ∈ R n(m+1) , u * [t] ∈ C([0, T], Δ m ( ), R nm ), and * ∈ R l , is said to be a solution to problem (8)- (11) if the functions u * r (t) are continuously differentiable on [ r−1 , r ), r = 1, m, and satisfy Equations (8), (10), and (11) with = * , = 1, m + 1, = * and initial conditions (9).…”

“…Various problems for LDEs and methods of solving them are studied in previous studies. [3][4][5][6][7][8][9][10][11] If ∈ R n and boundary condition (2) has the form…”

A Problem With Parameter for the Integro-Differential Equations

“…Particularly, in [21]- [22], they are used to describe the problems of long-term forecasting and control of groundwater level in the soil moisture. Various problems for these equations and methods for solving them are studied in [1,2,5,6,18,23]. The Fredholm integro-differential equation with a parameter has several features that should be considered when methods for research and solving problems with Equation (1.1) are created.…”

On the Initial-Boundary Value Problem for System of the Partial Differential Equations of Fourth Order

“…We will investigate the questions of existence and uniqueness of the classical solutions to the initial-boundary value problem for system of the partial differential equations of fourth order (1)--(5) and the approaches of constructing its approximate solutions. For this goals, we applied the method of introduction additional functional parameters proposed in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] for solving of various nonlocal problems for systems of hyperbolic equations with mixed derivatives. Considered problem is provided to nonlocal problem for the system of hyperbolic equations of second order including additional functions and integral relation.…”