• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제26권3호
• /
• pp.138-155
• /
• 2022

To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near $\frac{1}{2}$. Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.

• 대한수학회논문집
• /
• 제9권4호
• /
• pp.985-994
• /
• 1994

Boundary value problems are common in nature. Here we restrict our attention to the second order differential equations of the form $$ (1.1) \frac{d^2 y}{dx^2} = P(x)y(x) + Q(x), 0 \leq x \leq 1, $$ $$ y(0) = \alpha, $$ $$ y(1) = \beta, $$ where P(x) and Q(x) are continuous functions with $P(x) \geq 0, x \in [0, 1]$.

• Korean Journal of Mathematics
• /
• 제29권1호
• /
• pp.65-73
• /
• 2021

In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation L(f) = b (z) f + c (z), where L(f) is a linear differential polynomial and b (z), c (z) are entire functions and give some of its applications on sharing value problems.

• 대한수학회보
• /
• 제45권3호
• /
• pp.427-435
• /
• 2008

In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree $\bar{d}$(P) and lower degree $\underline{d}$(P).

• 대한수학회보
• /
• 제42권1호
• /
• pp.17-22
• /
• 2005

The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.

• Proceedings of the Jangjeon Mathematical Society
• /
• 제20권2호
• /
• pp.183-191
• /
• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• Journal of applied mathematics & informatics
• /
• 제6권1호
• /
• pp.143-162
• /
• 1999

In this paper we consider the second order generalized difference scheme for the two-point boundary value problem and ob-tain optimal order error estimates in $L^\infty$ and $W^{1,\infty}$ The results in this paper perfect the theory of the second order generalized difference method.

• 대한수학회논문집
• /
• 제39권1호
• /
• pp.117-125
• /
• 2024

In this paper, our focus is on exploring value sharing problems related to a transcendental entire function f and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Brück conjecture.

• Korean Journal of Mathematics
• /
• 제30권2호
• /
• pp.375-389
• /
• 2022

In this paper, we prove some fixed-point theorems in partially ordered fuzzy metric spaces for (𝜙, 𝜓, 𝛽)-Geraghty contraction type mappings which are generalization of mappings with Geraghty contraction type condition. Application of the derived results are shown in proving the existence of unique solution to some boundary value problems.

• 대한수학회보
• /
• 제51권5호
• /
• pp.1291-1297
• /
• 2014

In this paper, we investigate the value distribution of the difference operator on meromorphic functions, and obtain a difference analogue of a theorem of Hayman on meromorphic functions.