Approximation of the solution of the boundary value problem by the interpolation functional polynomial of the second order
Keywords:
інтерполяція, вузли інтерполяції, континуальна множина вузлів, поліноміальна інтерполяція функціоналівAbstract
The work considers a boundary value problem of the second order. For the approximate solution of this boundary value problem, an interpolation functional Newton polynomial of the second order is constructed on a continuous set of nodes. It is known that the fulfillment of the substitution rule is a necessary and sufficient condition for the specified polynomial to be interpolating for the solution of the boundary value problem on a continuous set of interpolating nodes. It is shown that the substitution rule holds for this functional Newton polynomial of the second order. To find the Green's function of the corresponding boundary value problem, we reduce it to Cauchy problems. The resulting differential equations have a piecewise constant coefficient, so it can be found in an explicit form. In this way, we obtain an interpolation functional polynomial of the Newton type of the second degree, which will be an approximation to the solution of the boundary value problem.
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