An approximate-analytical solution for the Hamilton–Jacobi–Bellman equation via homotopy perturbation method

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2Sirisubtawee1, Koonprasert2 2018Advances in Mathematical Physics460190View full textAdd to dashboardCite

“…Islam et al [45] demonstrated the application of the improved -expansion method with Riccati equation to obtain exact traveling wave solutions of (11). Their results were expressed in terms of the following functions: However, our obtained results in (20)- (27) are more generalized than the ones described above; i.e., selecting the appropriate constants and in our solutions can lead to the solutions obtained by other existing methods mentioned previously. Here we present the plots of the exact solution …”

“…The methods for obtaining exact explicit solutions of NPDEs are, for example, the ( / )-expansion method [6][7][8], the ( / , 1/ )-expansion method [9][10][11], the novel ( / )-expansion method [12], the tanh-function method [13], the exp-function method [14,15], the F-expansion method [16], Hirota's direct method [17,18], Kudryashov method [19,20], and the extended auxiliary equation method [21]. Examples of the methods for obtaining analytical approximate solutions to NPDEs are the variational iteration method [22,23] (VIM), the Adomian decomposition method [24,25] (ADM), the homotopy perturbation method [26,27] (HPM), and the reduced differential transform method [28]. In addition, the examples of useful methods for solving NPDEs numerically are the generalized finite difference method [29], the finite volume method [30], the finite element method [31], the spectral collocation method [32], and the Galerkin finite element method [33].…”

A Computational Method for Stochastic Optimal Control Problems in Financial Mathematics

“…For the purpose of illustration, the following parameters have been chosen [29]: r = 0.05, b = 0.11, = 0.1 and = 1 2 . In this case, selecting V 0 (t, x) = 2 √ x from the given initial condition yields the successive approximations: 2.073830084 2.0E−9 5 2.073830085 1.0E−9 6 2.073830086 0 Fig. 7.…”

An approximate method for solving a class of nonlinear optimal control problems

“…Shirazian and Effati in , used the modified variational iteration method (VIM) for nonlinear quadratic optimal control problems. In , homotopy perturbation method was studied and applied to solve optimal control problems. For some other techniques that can have been used for solving linear and nonlinear optimal control problems, we refer the interested reader to .…”