The Local Stability of Solutions for a Nonlinear Equation by Haibo Yan, Ls Yong

“…The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R) by assuming that the initial value only lies in the space L1(R)∩L∞(R).…”
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Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type by Alexandre F. Roch

“…We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.…”
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Nonlinear Vibration Analysis of Submerged Floating Tunnel Tether by Sheng-nan Sun, Zhi-bin Su, Yun-fen Feng

“…To study the nonlinear vibration characteristics of submerged floating tunnel tether, the nonlinear vibration partial differential equation of tether is set up, in which the inclination, sag, initial tension force, and length of tether are taken into account. …”
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Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System by Yang Zhao, De-Fu Cheng, Xiao-Jun Yang

“…The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.…”
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…Instead of solving the partial differential equation, we can find the optimal conditions for which the surface is the extremal of the Dirichlet functional. …”
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Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification by Li-Qun Chen, Hu Ding, C.W. Lim

“…The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. …”
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A New Proof of Central Limit Theorem for i.i.d. Random Variables by Zhaojun Zong, Feng Hu

“…Our main tool is the viscosity solution theory of partial differential equation (PDE).…”
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Positive Solutions for the Initial Value Problem of Fractional Evolution Equations by He Yang, Yue Liang

“…As an example, we study the partial differential equation of the parabolic type of fractional order.…”
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Uniqueness and radial symmetry for an inverse elliptic equation by B. Emamizadeh, M. H. Mehrabi

“…We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. …”
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Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation by Mohammad Mehdizadeh Khalsaraei, Ali Shokri, Zahra Mohammadnia, Hamid Mohammad Sedighi

“…In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. …”
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Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation by Letlhogonolo Daddy Moleleki, Chaudry Masood Khalique

“…We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. …”
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Finite Volume Element Approximation for the Elliptic Equation with Distributed Control by Quanxiang Wang, Tengjin Zhao, Zhiyue Zhang

“…In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. …”
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Pricing Parisian Option under a Stochastic Volatility Model by Min-Ku Lee, Kyu-Hwan Jang

“…A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.…”
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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd by Xichao Sun, Zhi Wang, Jing Cui

“…We study a stochastic partial differential equation in the whole space x∈ℝd, with arbitrary dimension d≥1, driven by fractional noise and a pure jump Lévy space-time white noise. …”
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An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing by R. Company, V. N. Egorova, L. Jódar

“…This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. …”
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Image Texture Analysis and Edge Detection Algorithm Based on Anisotropic Diffusion Equation by Xiaoqin Li

“…This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. …”
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Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition by Song Chol Kim, Song Guk Han, Yong Il Song, Jin Sim Kim, Myong Gun Hong

“…To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. …”
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Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition by Deniz Agirseven

“…Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. …”
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Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension by Ismail Kucuk, Kenan Yildirim

“…The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. …”
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New Results on the Noise Figure of HEMTs by M. A. Grado Caffaro, M. Grado Caffaro

“…The fundamental relationship that gives minimum noise figure is derived from a first-order linear partial differential equation, which is established by assuming reasonable statements based on experience.…”
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