The homotopy analysis method HAM is applied to solve linear and nonlinear fractional partial differential equations fPDEs . The fractional derivatives are described by Caputo’s sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given. The test examples, which include a variable coefficient, inhomogeneous and hyperbolic-type equations, demons...

Coupled nonlinear Schrödinger (CNLS) equations for the fiber couplers with asymmetric selfphase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, oneand two-soliton solutions are obtained for the constantand variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β2, S...

This thesis explores numerical methods for solving nonlinear partial differential equations (PDEs) that arise in option pricing problems. The goal is to develop or identify robust and efficient techniques that converge to the financially relevant solution for both one and two factor problems. To illustrate the underlying concepts, two nonlinear models are examined in detail: uncertain volatilit...

This paper studies the motion control of single-rod hydraulic actuators regulated by proportional directional control(PDC) valves with deadband and nonlinear flow gains. The boom motion control of a hydraulic robot arm driven by a singlerod hydraulic actuator is used as a case study. The experimental system dynamics are highly nonlinear. In addition, the system has large extent of modeling unce...