This paper introduces a highly effective method for solving third-order ordinary differential equations. The method employs a block backward formula to implement the primary scheme for numerical solutions. The numerical examples provided demonstrate its exceptional applicability and efficacy, outperforming existing methods and providing solutions that are nearly identical to exact solutions. This new method is unequivocally superior in solving third-order ordinary differential equations.
Key words: Differential equation, Initial Value Problem, Numerical method, Order, block backwards method.
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