Optical Solitons and Other Solutions to the (2+1)-Dimensional Cubic Nonlinear Schrödinger Equation with Fractional Temporal Evolution by Atas Sibel Sehriban, Sulaiman Tukur Abdulkadir, Bulut Hasan

“…The idea of conformable fractional derivative is used in transforming the complex nonlinear partial differential equation to nonlinear ordinary differential equation. …”
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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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An efficient numerical scheme for the study of equal width equation by Abdul Ghafoor, Sirajul Haq

“…In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. …”
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Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation by Adem Kilicman, Rathinavel Silambarasan

“…The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems yields the analytical solution. …”
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Simulation of Fingering Phenomena in Fluid Flow through Fracture Porous Media with Inclination and Gravitational Effect by H. S. Patel, R. Meher

“…Here we have studied the fingering phenomena in fluid flow through fracture porous media with inclination and gravitational effect and investigate the applicability of Adomian decomposition method to the nonlinear partial differential equation arising in this phenomena and prove the convergence of Adomian decomposition scheme, which leads to an abstract result and an analytical approximate solution to the equation. …”
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Vulnerable options pricing under uncertain volatility model by Qing Zhou, Xiaonan Li

“…By imposing additional conditions on the boundary condition and cutting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximate method for solving the fully nonlinear partial differential equation satisfied by the price of vulnerable options under the uncertain volatility model.…”
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Approximate solution of nonlinear Black–Scholes equation via a fully discretized fourth-order method by Azadeh Ghanadian, Taher Lotfi

“…In this work, a new fourth-order finite difference (FD) approximation (for both structured and unstructured grid of nodes) is contributed and equipped with the fourth-order Runge–Kutta scheme to tackle the financial nonlinear partial differential equation (PDE) of Black–Scholes. This timedependent PDE problem is converted to a set of ordinary differential equations (ODEs). …”
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Green's function of a centered partial difference equation by Richard Avery, Douglas Anderson

“…Applying a variation of Jacobi iteration we obtain the Green's function for the centered partial difference equation $$\Delta_{ww} u(x_{w-1},y_z) + \Delta_{zz} u(x_w,y_{z-1}) + f(u(x_w,y_z))=0,$$ which is the result of applying the finite difference method to an associated nonlinear partial differential equation of the form $$u_{xx}+u_{yy} +h(u)=0.$$ We show that approximations of the partial differential equation can be found by applying fixed point theory instead of the standard techniques associated with solving a system of nonlinear equations.…”
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One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity by Yasemin Şengül

“…In this note a one-dimensional nonlinear partial differential equation, which has been recently introduced by the author and co-workers, describing the response of viscoelastic solids showing limiting strain behaviour in strain and stress-rate cases is investigated. …”
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A Very Simple Procedure for Constructing the Solution of Nonlinear Elliptic PDEs (with Nonlinear Boundary Conditions) Arising from Heat Transfer Problems in Solids by Rogério Martins Saldanha da Gama

“…This work presents a procedure for constructing the solution of a second order nonlinear partial differential equation subjected to nonlinear boundary conditions in a very simple and systematic way. …”
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SOLUSI NUMERIK UNTUK PERSAMAAN NAVIER-STOKES DIMENSI DUA DENGAN METODE BEDA HINGGA by , VINALIA EKA WARDANI, , Dr. Sumardi M.Si.

“…Navier-Stokes equations are second order nonlinear partial differential equation that can be solved using finite difference method . …”

PERSAMAAN GELOMBANG AIR DANGKAL SATU DIMENSI DAN APLIKASINYA PADA MASALAH BENDUNGAN BOBOL by , NURDIANTI RIZKI HAPSARI, , Dr. Sumardi, M.Si.

“…The governing equation is in the form of a nonlinear partial differential equation system of order one. This governing equation is being applied for one dimensional dam break problem so that create a Riemann Problem. …”

A shooting argument approach to a sharp-type solution for nonlinear degenerate Fisher-KPP equations by SanchezGarduno, F, Maini, P, Kappos, M

“…Associated with this connection is a sharp-type solution of the nonlinear partial differential equation.…”

Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation by Chapman, S, Howls, C, King, J, Daalhius, A

“…The formation of shocks in waves of advance in nonlinear partial differential equations is a well-explored problem and has been studied using many different techniques. …”

Control of bifurcation structures using shape optimization by Boullé, N, Farrell, PE, Paganini, A

“…We propose a numerical technique for controlling the bifurcation diagram of a nonlinear partial differential equation by varying the shape of the domain. …”

A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations by Sánchez-Garduño, F, Kappos, E, Maini, P

“…Associated with this connection is a sharp-type solution of the nonlinear partial differential equation.…”

Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation by Chapman, S, Howls, C, King, JR, Olde Daalhuis, AB

“…The formation of shocks in waves of advance in nonlinear partial differential equations is a well-explored problem and has been studied using many different techniques. …”

Hirota bilinear computation of multi soliton solutions korteweg de vries equation by Hamdan, Anniza

“…Soliton is the solution of nonlinear partial differential equation that exists due to the balance between nonlinearity and dispersive effects. …”
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Application of similarity solution on gaseous pollutant problems by Ng, Sin Yi

“…By introducing of similarity variables, the nonlinear partial differential equation can be reduced to a second order differential equation. …”
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An analytical method for solving exact solutions of the convective heat transfer in fully developed laminar flow through a circular tube by Belhocine, A., Wan Omar, W. Z.

“…This paper proposes an exact solution to the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions, and one initial condition. …”