Eine Methode zur näherungsweisen Lösung einer Randwertaufgabe einer linearen gewöhnlichen Differentialgleichung 2. Ordnung (Q797974)

A numerical method is presented for solving the two-point boundary value problem \(x''(t)-a(t)x(t)=g(t), x(-1)=x_{-1}\), \(x(1)=x_ 1\). The problem is transformed by special integral operators \(K_ i\) and \(T_ i\) to an integral equation of Volterra-Fredholm-type. These operators are defined on such a way that the relations \(K_ iax=T_{i+1}x+K_{i+1}x'' (i=0,1,2,...)\) are satisfied. By neglecting the residual \(K_ nax\), which is estimated, the authors give an integral equation of Fredholm type with degenerated kernel if a(t) is a polynomial. These statements are proved, the corresponding integral equations as well as some examples are given.