ABSTRACT This study investigates the solution of an ill‐posed time‐fractional order Schrödinger equation using a mollification regularization technique Dirichlet kernel. The regularized is obtained through convolution kernel with real measured data. Estimations convergence are derived based on parameter selection criteria priori and posteriori. efficiency methodology was successfully verified by simulation tests.

We study the inverse issues for heat equations with spatial‐dependent source and time‐dependent source, respectively. In this work, identification are ill‐posed, numerical solutions (if they exist) not continuously dependent on data. A mollification regularization method Dirichlet kernel is proposed to tackle presented problems. Convergence analyses carried out via two parameter selection rules (a priori a posteriori), Ultimately, series of experiments verify our theoretical results.

We consider solving the Cauchy problem of Schrödinger equation with potential-free field by a mollification regularization method in this work. By convolving measured data Dirichlet kernel, ill-posed case is turned into well-posed one. Convergent estimates are gained via priori and posteriori parameter selection rules. Finally, three simulation experiment results shown to prove feasibility stability our presented procedure.

In this paper, the ill-posed problem of two-dimensional modified Helmholtz equation is investigated in a strip domain. For obtaining stable numerical approximation solution, mollification regularization method with de la Vallée Poussin kernel proposed. An error estimate between exact solution and given under suitable choices parameter. Two experiments show that our procedure effective respect to perturbations data.

In this paper, the ill-posed Cauchy problem for Helmholtz equation is investigated in a strip domain. To obtain stable numerical solution, mollification regularization method with Dirichlet kernel proposed. Error estimate between exact solution and its approximation given. A experiment of interest shows that our procedure effective respect to perturbations noise data.

The purpose of this work is to create an identical approximate regularization method for solving a Cauchy problem two‐dimensional heat conduction equation. severely ill‐posed. convergence rates are obtained under priori parameter choice rule. Numerical results presented two examples with smooth and continuous but not boundaries compared the solutions which displayed in text. numerical show that our effective, accurate, stable solve ill‐posed problems.

In this paper, two Cauchy problems of Helmholtz equation in a three-dimensional case are considered. To address these problems, mollification method with bivariate Dirichlet kernel is proposed. Stable errors estimates obtained based on appropriate priori choices parameters. Convergence show that the regularization solution depends continuously data and wavenumber. Numerical examples our interest more effective than Gaussian under same parameter selection rule, procedure stable respect to...

In this paper, a Cauchy problem of Helmholtz equation in multi-dimensional case is investigated. This severely ill-posed and small perturbations to measurement data can result large changes the solution. A kind operator regularization method proposed. The stable error estimates are obtained L2−norm Hr−norm under conditions that m even, md>x, mk>1, suitable choice regular parameters. Error show regularized solution depends continuously on perturbation noisy wave number. Our makes up...

In this article, an inverse problem with regards to the Laplace equation non-homogeneous Neumann boundary conditions in a three-dimensional case is investigated. To deal problem, regularization method (mollification method) bivariate de la Vallée Poussin kernel proposed. Stable estimates are obtained under priori bound assumptions and appropriate choice of parameter. The error indicate that solution approximation continuously depends on noisy data. Two experiments presented, order validate...

Summary Sparse deconvolution methods frequently invert for subsurface reflection impulses and adopt a trace-by-trace processing pattern. However, following this approach causes unreliability of the estimated reflectivity due to nonuniqueness inverse problem, poor spatial continuity structures in reconstructed section, suppression on signals with small amplitudes. We have developed structurally constrained multichannel (SCMD) algorithm alleviate these three issues. The inverts high-resolution...

In this paper, an identical approximate regularization method is extended to the Cauchy problem of two-dimensional heat conduction equation, kind severely ill-posed. The convergence rates are obtained under a priori parameter choice rule. Numerical results presented for two examples with smooth and continuous but not boundaries, compared solutions which displayed in paper. numerical show that our effective, accurate stable solve ill-posed problems.