On the number of single-peak solutions of the nonlinear Schrödinger equation
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the Numerical Integration of the Heat Equation.
On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems
Karátson and Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type, see J. Karátson, S. Korotov (2009). The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the technical and numerical aspects and on the components of the error estimation, especially on the adequate...
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.
On the numerical solution of fractional hyperbolic partial differential equations.
On the numerical solution of nonlinear partial differential equations on divergence form
On the numerical solution of some semilinear elliptic problems.
On the numerical solution of the diffusion equation with a nonlocal boundary condition.
On the Numerical Solution of the Equation ....-(....) = f and Its Discretizations, I.
On the numerical solution of the first biharmonic equation
On the numerical solution of the one-dimensional convection-diffusion equation.
On the numerical solutions of convection-diffusion equations
On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy...
On the one class of hyperbolic systems.
On the operator related to Bessel heat equation.
On the Operator Solutions of Difference Equations
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.