Abstract
Purpose
– In this article, the author proposed a new analytical solution procedure for 12 order differential equation. The new analytical technique namely homotopy analysis transform method is efficient and effective for solving higher order differential equations. The results indicate the effectiveness and stability of the proposed algorithm. The paper aims to discuss these issues.
Design/methodology/approach
– The author designed a new solution methodology for higher order differential equations which is a combination of Laplace transformation and homotopy deformation theory.
Findings
– The author mainly discussed two numerical applications with error analysis of analytical scheme which shows high order accuracy of the projected technique which will serve as a milestone for solving higher order differential equations in engineering with no efforts.
Originality/value
– The author proposed an innovative and original idea for nth-order differential equations in this article.