Solutions of Smooth Nonlinear Partial Differential Equations by Jan Harm van der Walt

“…The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions. …”
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On closed-form solutions of some nonlinear partial differential equations by S. S. Okoya

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Solving Nonlinear Partial Differential Equations by the sn-ns Method by Alvaro H. Salas

“…We present the application of the sn-ns method to solve nonlinear partial differential equations. We show that the well-known tanh-coth method is a particular case of the sn-ns method.…”
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Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application by Xiao-Feng Yang, Yi Wei

“…The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. …”
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New Exact Solutions for New Model Nonlinear Partial Differential Equation by A. Maher, H. M. El-Hawary, M. S. Al-Amry

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Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations by Khaled A. Gepreel, Taher A. Nofal, Fawziah M. Alotaibi

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Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations by Jun Shuai, Xuli Han

“…However, the neglectful modes representing only a tiny amount of energy will be crucial in the modeling for certain type of nonlinear partial differential equations (PDEs). In this paper, an optimal combination of EEFs is proposed for model reduction of nonlinear partial differential equations (PDEs), obtained by the basis function transformation from the initial EEFs. …”
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Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations by Fukang Yin, Junqiang Song, Xiaoqun Cao, Fengshun Lu

“…This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. …”
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Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order by Veyis Turut, Nuran Güzel

“…Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. …”
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Conservation Laws for Some Systems of Nonlinear Partial Differential Equations via Multiplier Approach by Rehana Naz

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Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method by Shailesh A. Bhanotar, Mohammed K. A. Kaabar

“…In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. …”
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Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method by Ömer Faruh Gözükızıl, Hami Gündoğdu

“…And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. …”
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New solutions to a category of nonlinear PDEs by Bacui Li, Fuzhang Wang

“…The nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. …”
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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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Nonlinear elliptic problems with the method of finite volumes by Sanjay Kumar Khattri

“…Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. …”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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The Rayleigh quotient and dynamic programming by Richard Bellman

“…The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. …”
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Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of (2+1)-dimensional nonlinear partial differential equation. The resulting theory is applied to the (2+1)-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. …”
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Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…This paper investigates both the transient and the steady state of a one-step nth-order oxidation exothermic reaction in a slab of combustible material with an insulated lower surface and an isothermal upper surface, taking into consideration reactant consumption. The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. …”
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An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation by Chaeyoung Lee, Jintae Park, Soobin Kwak, Sangkwon Kim, Yongho Choi, Seokjun Ham, Junseok Kim

“…The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. …”
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