Modified Abbasbandy’s method free from second derivative for solving nonlinear equations

The boundary value problems in Kinetic theory of gases, elasticity and other applied areas are mostly reduced in solving single variable nonlinear equations. Hence, the problem of approximating a solution of the nonlinear equations is important. The numerical methods for finding roots of such equations are called iterative methods. There are two type of iterative methods in literature: involving higher derivatives and free from higher derivatives. The methods which do not require higher derivatives have less order of convergence and the methods having high convergence order require higher derivatives. The aim of present report is to develop an iterative method having high order of convergence but not involving higher derivatives. We propose three new methods to solve nonlinear equations and solve text examples to check validity and efficiency of our iterative methods.