A linear Multistep Block Hybrid Method with four off-grid points is presented for the direct approximation of the solution of fourth order Boundary Value Problems. Multiple Finite Difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem, without the need to reduce it previously to a first-order system. The convergence of the proposed method is discussed. The superiority of this method over existing methods is established numerically considering different problems that have appeared in the literature.

中文翻译：

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四阶边值问题数值解的块混合法

提出了具有四个离网点的线性多步块混合方法，用于直接逼近四阶边值问题的解。导出多个有限差分公式并将其分组到一个唯一的块中，以形成一个数值积分器来直接解决四阶问题，而无需事先将其简化为一阶系统。讨论了该方法的收敛性。考虑到文献中出现的不同问题，从数值上确定了该方法相对于现有方法的优越性。