NUMERICAL IMPLEMENTATION OF SOLVING A BOUNDARY VALUE PROBLEM FOR A SYSTEM OF LOADED DIFFERENTIAL EQUATIONS WITH PARAMETER - A.T.Assanova; E.A.Bakirova; Zh.M.Kadirbayeva (Academic Scientific Journal of Computer Science, 2019)
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.