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Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.

applied mathematics

Five Steps Block Predictor-Block Corrector Method for the Solution of &amp;lt;i&amp;gt;y''&amp;lt;/i&amp;gt; = &amp;lt;i&amp;gt;f&amp;lt;/i&amp;gt; (&amp;lt;i&amp;gt;x&amp;lt;/i&amp;gt;,&amp;lt;i&amp;gt;y&amp;lt;/i&amp;gt;,&amp;lt;i&amp;gt;y'&amp;lt;/i&amp;gt;)