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The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that the Regula-Falsi method always gives guaranteed results but slow convergence. However, the Newton–Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton–Raphson method is, it fails when first derivative is zero or approximately zero.

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