Purpose -The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind. Design/methodology/approach -The method converts the nonlinear integral equation into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate. Findings -The proposed technique allows the authors to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well-suited for solving nonlinear integral equations.Originality/value -The present approach provides a reliable technique that avoids the difficulties and massive computational work if compared with the traditional techniques and does not require discretization in order to find solutions to the given problems.

Purpose -The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs). Design/methodology/approach -The method converts the nonlinear BVP into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate. Findings -The proposed technique allows us to obtain an approximate solution in a series form which satisfies all the given conditions. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations with initial and boundary conditions. Originality/value -The paper provides a reliable technique which avoids the tedious work needed by classical techniques and existing numerical methods and does not require discretization in order to find the solutions of the given problems.

Purpose -The purpose of this paper is to present a method for solving nonlinear integro-differential equations with constant/variable coefficients and with initial/boundary conditions. Design/methodology/approach -The method converts the given problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate. Findings -The proposed technique allows an approximate solution in a series form to be obtained. Test problems are solved to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear integro-differential equations. Originality/value -The present approach provides a reliable technique which avoids the tedious work needed by the classical techniques.

PurposeThe purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary conditions.Design/methodology/approachThe method converts the nonlinear boundary value problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.FindingsThe proposed technique allows us to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations.Originality/valueThe present approach provides a reliable technique, which avoids the tedious work needed by classical techniques and existing numerical methods. The nonlinear problem is solved without linearizing or discretizing the nonlinear terms of the equation. The method does not require physically unrealistic assumptions, linearization, discretization, perturbation, or any transformation in order to find the solutions of the given problems.