The mollification method based on a modified operator to the ill-posed problem for 3D Helmholtz equation with mixed boundary
Copyright policy )The mollification method based on a modified operator to the ill-posed problem for 3D Helmholtz equation with mixed boundary
In this work, a Cauchy problem for the 3D Helmholtz equation with mixed boundary is studied. The mollification method based on modified bivariate de la Vallée Poussin operator to solve the stated Cauchy problem is used. It is verified that the considered method is stable. The paper is organized as follows. Section 1 is an introduction. In Section 2, the ill-posedness of the considered problem is illustrated. The modified bivariate de la Vallée Poussin kernel and its certain properties are presented in Section 3. This is also used to construct the mollification operator to obtain the regularization solution. Section 4 is devoted to the stable convergence estimates under the suitable choices of regularization parameters in \(0
- Minzu University of China China (People's Republic of)
- Hebei Normal University of Science and Technology China (People's Republic of)
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, Numerical methods for inverse problems for boundary value problems involving PDEs, mollification method, Ill-posed problems for PDEs, 3D Helmholtz equation, error estimate, Stability and convergence of numerical methods for boundary value problems involving PDEs, ill-posed, modified de la Vallée Poussin operator, Numerical methods for ill-posed problems for boundary value problems involving PDEs
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, Numerical methods for inverse problems for boundary value problems involving PDEs, mollification method, Ill-posed problems for PDEs, 3D Helmholtz equation, error estimate, Stability and convergence of numerical methods for boundary value problems involving PDEs, ill-posed, modified de la Vallée Poussin operator, Numerical methods for ill-posed problems for boundary value problems involving PDEs
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