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Разностная схема 4-го порядка точности для дифференциального уравнения с переменными коэффициентами

Гордин В. А., Цымбалов Е. А.

We present compact difference scheme on three-point stencil for unknown function. The scheme approximates linear second order differential equation with variable smooth coefficient. Our numerical experiments confirmed 4-th accuracy order of solutions of the difference scheme and of eigenvalues’ approximation for the boundary problem. The difference operator is almost self-conjugate, and its spectrum is real. The Richardson extrapolation method improves the accuracy order.