In this paper

an improved secant method is given to solve the equations with non-differential terms.In the iterative process

this method uses the different quotient to replace the derivative value without calculating it.Under the γ-condition

the convergence theorem is proven and the error estimation is obtained by the technique of major function sequences.The result is as follows: If α satisfies some condition

then the sequences{zn}

{wn}produced by the iteration scheme given in the paper

converge to the sol...