Yildirim Ozdemir

On nonlocal boundary value problems for hyperbolic-parabolic equations

A numerical method is proposed for solving the hyperbolic-parabolic partial differential equations with nonlocal boundary condition. The first and second order of accuracy difference schemes are presented. The method is illustrated by numerical examples.

A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations

The nonlocal boundary value problem ð ‘‘ 2 ð ‘¢ ( ð ‘i ) / ð ‘‘ ð ‘i 2 + ð ´ ð ‘¢ ( ð ‘i ) = ð ‘“ ( ð ‘i ) ( 0 ≤ ð ‘i ≤ 1 ) , ð ‘– ( ð ‘‘ ð ‘¢ ( ð ‘i ) / ð ‘‘ ð ‘i ) + ð ´ ð ‘¢ ( ð ‘i ) = ð ‘” ( ð ‘i ) ( − 1 ≤ ð ‘i ≤ 0 ) , ð ‘¢ ( 0 + ) = ð ‘¢ ( 0 − ) , ð ‘¢ ð ‘i ( 0 + ) = ð ‘¢ ð ‘i ( 0 − ) , ð ´ ð ‘¢ ( − 1 ) = ð ›¼ ð ‘¢ ( 𠜇 ) + 𠜑 , 0 < 𠜇 ≤ 1 , for hyperbolic Schrodinger equations in a Hilbert space ð » with the self-adjoint positive definite operator ð ´ is considered. The stability estimates for the solution of this problem are established. In applications, the stability estimates for solutions of the mixed-type boundary value problems for hyperbolic Schrodinger equations are obtained.

On numerical solutions for hyperbolic–parabolic equations with the multipoint nonlocal boundary condition

Abstract A numerical method is proposed for solving multi-dimensional hyperbolic–parabolic differential equations with the nonlocal boundary condition in t and Dirichlet and Neumann conditions in space variables. The first and second order of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic–parabolic differential equations with variable coefficients in x and two-dimensional hyperbolic–parabolic equation.

On numerical solution of multipoint NBVP for hyperbolic-parabolic equations with Neumann condition

A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Neumann condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic differential equations with variable in x coefficients.

Numerical solution of hyperbolic-Schrödinger equations with nonlocal boundary condition

A numerical method is proposed for solving hyperbolic-Schrodinger partial differential equations with nonlocal boundary condition. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional hyperbolic-Schrodinger partial differential equation. The method is illustrated by numerical examples.

A NOTE ON DIFFERENCE SCHEMES OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC‐PARABOLIC EQUATIONS

A numerical method is proposed for solving multi‐dimensional hyperbolic‐parabolic differential equations with the nonlocal boundary condition in t and Dirichlet condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first‐ and second‐orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one‐dimensional hyperbolic‐parabolic partial differential equations with variable in x coefficients.