• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.337-348
• /
• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.169-189
• /
• 2020

A common fixed point result for weakly increasing mappings satisfying generalized contractive type in ordered partial S-metric spaces are derived. Also as an application of our results we consider a couple integral equations.to guarantee the existence of a common solution.

• Korean Journal of Mathematics
• /
• v.28 no.1
• /
• pp.17-30
• /
• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.293-300
• /
• 1998

The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernels using the Toeplitz matrices. The solution has a computing time requir-ment of O(N2) where 2N+1 is the number of discretization points used. Also the error estimate is computed. Some numerical Exam-ples are computed using the Mathcad package.

• Honam Mathematical Journal
• /
• v.26 no.4
• /
• pp.455-462
• /
• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.65-78
• /
• 1999

We present a fast/parallel Poisson solver on disks, based on efficient evaluation of the exact solution given by the Newtonian potential and the Poisson integral. Derived from an integral formula-tion it is more accurate and simpler in parallel implementation and in upgrading to a higher order algorithm than an algorithm which solves the linear system obtained from a differential formulation.

• Journal of Biomedical Engineering Research
• /
• v.11 no.1
• /
• pp.89-96
• /
• 1990

The numerical evaluation of Rayleigh's integral for the sound source reconstruction can be speeded up by the use of angular frequency propagation method and the FFT. However, are several source of errors involved during the reconstruction. Besides the aliasing error due to undersampling in space, the wrap around error. which is caused by undersampling the kernel functionin frequency domain, and windowing effect are present. We found that there is no replicated source problem and the windowing effect is due to the windowing the kernel function In frequency domain, and, xero padding is always required to improve the quality of reconstruction.

• The Pure and Applied Mathematics
• /
• v.27 no.3
• /
• pp.109-124
• /
• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.4
• /
• pp.763-769
• /
• 2014

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.141-152
• /
• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.