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This work presents the extension of the Residual Power Series Method (RPSM) to boundary value problems using Mathematica software. This development is tested on twelfth-order linear and non-linear boundary value problems. The residual analysis and solutions are designed through tables and figures. The results show a very strong agreement with the exact solution and the comparison of the results with the other well-known methods shows the superiority of this method.

The solution of twelfth order boundary value problems by the improved residual power series method: new approach