求解具有跳跃条件的两区间Sturm-Liouville问题的广义有限差分法

S. Çavuşoğlu, O. Mukhtarov
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引用次数: 0

摘要

考虑一个Sturm-Liouville问题,该问题定义在两个不相交的区间上,并具有跨越这些区间公共端点的附加跳跃条件。基于有限差分法(FDM),提出了一种求解这类非标准边值问题的新方法。为了证明所提出的FDM泛化方法的适用性和有效性,我们解决了一个简单但具有说明性的例子。得到的数值解与相应的精确解进行了图解比较。
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Generalized finite difference method for solving two-interval Sturm-Liouville problems with jump conditions
We consider a Sturm-Liouville problem defined on two disjoint intervals together with additional jump conditions across the common endpoint of these intervals. Based on Finite Difference Method (FDM) we have developed a new tecnique for solving such type nonstandard boundary value problems (BVP). To show applicability and effectiveness of the proposed generalization of FDM, we solved a simple but illustrative example. The obtained numerical solutions are graphically compared with the corresponding exact solutions.
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