NUMERICAL IMPLEMENTATION OF SOLVING A BOUNDARY VALUE PROBLEM FOR A SYSTEM OF LOADED DIFFERENTIAL EQUATIONS WITH PARAMETER
Ключевые слова:
boundary value problem with parameter, loaded differential equation, numerical method, algorithm.Аннотация
A linear two-point boundary value problem for the loaded differential equations with parameter is
considered. This problem is investigated by parameterization method. We offer algorithm for solving to boundary
value problem for the system of loaded differential equations with parameter. In first, original problem is reduced to
equivalent problem consisting the Cauchy problems for system of ordinary differential equations with parameters in
subintervals and functional relations with respect to introduced additional parameters. At fixed values of parameters
the Cauchy problem for system of ordinary differential equations in subinterval has a unique solution. This solution
is represented with fundamental matrix of system. Using these representations we compile a system of linear
algebraic equations with respect to parameters. We proposed algorithm for finding of numerical solution to the
equivalent problem. This algorithm includes of the numerical solving of the Cauchy problems for system of the
ordinary differential equations and solving of the linear system of algebraic equations. For numerical solving of the
Cauchy problem we apply the Runge–Kutta method of 4th order. The proposed numerical implementation is
illustrated by example.
