In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.

In this paper, we developed a new variational iteration method using the quasilinearization and Adomian polynomial to solve nonlinear differential equations. The convergence analysis of our is also discussed under Lipschitz continuity condition in Banach space. Some application problems are included test efficacy proposed method. behavior investigated for different values parameter t. This powe...

The method of upper and lower solutions and the method of quasilinearization for a second order nonlinear differential equation −x (t) = f (t, x, x ), t ∈ [0, 1] subject to the separated boundary conditions p0x(0) − q0x (0) = a, p1x(1) + q1x (1) = b, is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained....

Optimal boundary control of semilinear parabolic equations requires efficient solution methods in applications. Solution methods bypass the nonlinearity in different approaches. One approach can be quasilinearization (QL) but its applicability is locally in time. Nonetheless, consecutive applications of it can form a new method which is applicable globally in time. Dividing the control problem ...