I think that this expresses your intent: In this section, thirteen examples are presented in order to illustrate the accuracy and efficiency of the developed method. For the first- to third-order BDE problems, the results were obtained using the methods in Madrid (2003) . For the fourth- to ninth-order BDE problems, we compare results obtained by using our direct method with Madrid's method by reducing them first to a system of first-order BDEs.
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