IMA Journal of Applied Mathematics · 1979 · 48 citations · 0 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsDifferential EquationsBoundary ConditionsConvergence AnalysisFinite Difference MethodsNumerical AlgorithmsNumerical Methods For Differential EquationsNumerical StabilityFinite Difference DiscretizationFinite Difference SchemesOrder Convergence
We present a sixth-order finite difference method for the general second-order non-linear differential equation Y“=f(x, y, y') subject to the boundary conditions y(a) = A, y(b) = B. In the case of linear differential equations, our finite difference scheme leads to tridiagonal linear systems. We establish, under appropriate conditions, O(h6)-convergence of the finite difference scheme. Numerical examples are given to illustrate the method and its sixth-order convergence.