An effective operational matrix method for the solution of non-linear third-order initial value problems

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Abstract The present paper provides a new technique using the clique polynomials as basis function for the operational matrices to obtain numerical solutions of third-order non-linear ordinary differential equations. It aims to find all solutions as easy as possible. Numerical results derived using the proposed techniques are compared with the exact solution or the solutions obtained by other existing methods. The new numerical examples were examined to show that the new approach is highly efficient and accurate. The approximate solutions can be very easily calculated using computer program Matlab. Communicated Editor: M. Berbiche. Manuscript received Oct 27, 2024; revised April 24, 2025; accepted May 11, 2025; published June 14, 2025.References [1] Agarwal, R. P. (1986). Boundary value problems from higher order differential equations. World Scientific.‏ Search in Google Scholar. View a Book [2] Adesanya, A. O., Udoh, D. M., & Ajileye, A. M. (2013). 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