• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.133-143
• /
• 2014

A new three-step quadraparametric family of eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear equation. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.367-372
• /
• 2012

Taking the integrated Chebyshev-type counting function of the appropriate order, we improve the error term in Park's prime geodesic theorem for hyperbolic manifolds with cusps. The obtained estimate coincides with the best known result in the Riemann surfaces case.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.705-714
• /
• 2002

We consider a jump-diffusion model generated by a Levy process for an asset price. We present an error estimate for the option prices between the jump-diffusion model and the Black-scholes model when the former converges weakly to the latter.

• Communications of the Korean Mathematical Society
• /
• v.20 no.2
• /
• pp.405-409
• /
• 2005

In [1], Sharma and Goel obtained a bound for random error correcting codes with Lee weight considerations. The purpose of this paper is to first point out a discrepancy in this result and then give a correct version of the same, improving upon the bound tremendously.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.1081-1098
• /
• 2006

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.897-915
• /
• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.291-303
• /
• 2014

In this paper, through a direct computation with subintervals partitioning [0, 1], we compute better a posteriori bounds for the average case error of the difference between the true value of $I(f)=\int_{0}^{1}f(x)dx$ with $f{\in}C^r$[0, 1] minus the composite trapezoidal rule and the composite trapezoidal rule minus the basic trapezoidal rule for $r{\geq}3$ by using zero mean-Gaussian.

• East Asian mathematical journal
• /
• v.31 no.5
• /
• pp.685-693
• /
• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Honam Mathematical Journal
• /
• v.15 no.1
• /
• pp.105-120
• /
• 1993

The auxiliary principle technique is used to prove the uniqueness and the existence of solutions for a class of nonlinear variational inequalities and suggest an innovative iterative algorithm for computing the approximate solution of variational inequalities. Error estimates for the finite element approximation of the solution of variational inequalities are derived, which refine the previous known results. An example is given to illustrate the applications of the results obtained. Several special cases are considered and studied.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.661-672
• /
• 1997

In this paper we introduce the semidiscrete solution of a single-phase nonlinear Stefan problem We analyze the optimal convergence of the semidiscrete solution in $H^1$ and $H^2$ normed spaces and also we derive the error estimates in $L^2$ normed space.