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All Journal MATEMATIKA Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains Journal of Science and Applicative Technology
Warsoma Djohan
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Institut Teknologi Bandung
Civil Engineering, Building, Construction & Architecture Earth & Planetary Sciences Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering

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Dinamika Gelombang Cnoidal di Atas Dasar Tak Rata Menggunakan Persamaan Gelombang Dua Arah Boussinesq Warsoma Djohan
Jurnal Matematika & Sains Vol 2, No 2 (1997)
Publisher : Institut Teknologi Bandung

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Abstract

Waves over uneven bottom which are running in two directions are governed by Boussinesq equations. When the bottom is flat, the Boussinesq equations have a periodic travelling wave solution, i.e. a solution which is running undisturbed in shape and velocity. This travelling wave is called a cnoidal wave. In this research the distortion of a cnoidal wave due to decreasing depth will be studied numerically. A cnoidal wave is initially running above flat bottom, then the depth decreases and flat again with depth h1 (< h0). First, a cnoidal wave is constructed as solution of the constrained critical point problem, i.e. finding the extremism of energy with constraints momentum and mass. Then the Boussinesq equations are discritized using the direct Fourier truncation method. Numerical simulation shows that the cnoidal wave constructed above is indeed a travelling wave solution. By choosing h1 to be the eigendepth of the two-soliton solution of KdV according to the inverse scattering theory, numerical simulations show the splitting process of an initial cnoidal wave into two waves.
METODA BEDA HINGGA PADA PERSAMAAN KDV GELOMBANG INTERFACE Wiryanto, L.H; Djohan, Warsoma
MATEMATIKA Vol 9, No 1 (2006): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Propagation of interfacial wave, modeled in an equation of KdV type, is solved numerically. A finite different method is used to construct a system of linear equations from the model, and the system is solved by Gauss-Seidel method. This numerical procedure is firstly tested for solitary wave, which gives agreement to the analytical solution, and is then used to observe a simulation of wave propagation generated on the left by a generator, for some various values of parameters, depth and fluid density
Fourth Order PDE: Model of Thin Film Flow Involving Surface Tension Wiryanto, Leo Hari; Djohan, Warsoma
Journal of the Indonesian Mathematical Society Vol. 31 No. 2 (2025): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i2.1454

Abstract

Surface wave on thin film is considered by involving surface tension. The fluid flows on an inclined channel. The model is based on lubrication theory, and presented in a single equation of the thickness of the fluid as wave movement, and the equation is strongly nonlinear. In solving the model, scaling and linearized processes are applied. So that three physical parameters play an important role in the wave propagation: bottom inclination, length of the scaling and the surface tension. Each of those parameters is represented as a term in the equation. Then, the equation is solved numerically by an implicit finite difference method for the linearized equation, so that the solution can be used to observe the effect of those physical quantities. We found that the surface wave propagates with different speed and reducing the amplitude. When the surface tension is involved, the profile of the wave slightly changes, beside it also effect to the movement of the wave. This is simulated in this paper.
OPTIMIZATION OF FUNCTION OF TWO VARIABLES, A NUMERICAL APPROACH Wiryanto, Leo Hari; Djohan, Warsoma
Journal of Science and Applicative Technology Vol. 8 No. 1 (2024): Journal of Science and Applicative Technology June Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/jsat.v8i1.1855

Abstract

Teaching development in maximum value of a function of two variables is reported in this paper. Based on an experience in teaching numerical method, difficulty in determining step size of steepest ascent gives an idea to covert the function into one variable, so that we can solve numerically by standar method for that function, such as Newton method. Here, we present some examples to support that development.
Co-Authors L.H Wiryanto Leo Hari Wiryanto Leo Hari Wiryanto, Leo Hari