we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation 4(f(3x + y) + f(3x− y)) = −12(f(x + y) + f(x− y)) + 12(f(2x + y) + f(2x− y))− 8f(y)− 192f(x) + f(2y) + 30f(2x).

Using the fixed point method, we prove the generalized HyersUlam stability of the following cubic-quartic functional equation f(2x+ y) + f(2x− y) = 3f(x+ y) + f(−x− y) + 3f(x− y) + f(y − x) (0.1) + 18f(x) + 6f(−x)− 3f(y)− 3f(−y) in fuzzy Banach spaces.

In this paper, we prove the generalized Hyres–Ulam–Rassias stability of the mixed type cubic and quartic functional equation f (x + 2y) + f (x − 2y) = 4(f (x + y) + f (x − y)) − 24f (y) − 6f (x) + 3f (2y) in non-Archimedean ℓ-fuzzy normed spaces.

In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x− 2y) = 4f(x + y) + 4f(x− y)− 6f(x) + f(2y) + f(−2y)− 4f(y)− 4f(−y) in non-Archimedean Banach spaces.

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.

and Applied Analysis 3 is called a quadratic functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic mapping. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof 7 for mappings f : X → Y , where X is a normed space and Y is a Banach space. Cholewa 8 noticed that the theorem of Skof is still...

The cubic vortical Whitham equation is a model for wave motion on vertically sheared current of constant vorticity in shallow inviscid fluid. It generalizes the classical by allowing and adding nonlinear term. inclusion this extra term allows to admit periodic, traveling-wave solutions with larger amplitude than equation. Increasing leads as well. stability these examined numerically. All moder...