Journal of Applied and Computational Sciences

EFFECT OF BOUNDARY CONDITIONS ON WAVE MODELING THROUGH FINITE DIFFERENCE METHOD

Timur Koparan — 2022-06-30

The underground effect of a structure with known geometric, velocity and density parameters can be defined as modelling. The purpose of the modelling is to determine the complexity in-ground structure. For this, artificial seismogram models have been constructed. Most commonly, methods based on the numerical solution of wave equations have been used. In these methods, the source can be placed at any point of the studied geometry and instantaneous energy emanations (snap-shots) can be taken at any desired time. Hence it can be shown how the wave field moves in the ground. In this study, two- and three-dimensional scalar wave equations are modelled with the finite difference method (FDM) in the light of previously known theoretical knowledge, and it is shown how the wave field behaves in the medium by using different mathematically investigated boundary conditions. In the numerical solutions obtained by the program codes written in FORTRAN, Dirichlet and absorbing boundary conditions were used separately, and the effect of boundary conditions was revealed as snap-shot and artificial seismograms via GRAPHER and MATLAB programs.

HIGHER ORDER QUASI CUBIC B-SPLINE SOLUTION OF ADVECTION EQUATION

Mehmet Ali Mersin — 2022-06-30

In this study, the Advection equation (AE) will be solved numerically by using the high order method based on cubic B-spline quasi-interpolation for space discretization and second and fourth order single step method for time discretization. The test problem is studied, and accuracy of the numerical results are measured by the computing the maximum error norm and rate of convergence for the proposed two methods.

FACTORS DETERMINING THE DEVELOPMENT OF MINIMUM COMPARABLE AREAS AND SPATIAL INTERACTION

Muhammet Ensar Yesilyurt — 2022-06-30

One popular strand of literature concerning economic growth and/or GDP focuses on the growth/GDP of minimum comparable areas (MCAs) but conducting research in this area is difficult due to data problems. To understand the nature of the microlevel structure, we estimate the determinants of the GDP of MCAs in Turkey since no single study covers all towns. We use spatial models and show that regional development policies should be based on the actual contiguity of MCAs, which is not currently considered in policies. We utilize Bayesian criteria to determine the best-fitting spatial weight matrix, whereas many previous studies have chosen such matrices subjectively.

THE TRAVELLING SALESMAN PROBLEM SOLUTION BY MIXED INTEGER LINEAR PROGRAMMING IN MATLAB CODE

Jaromír Zahrádka — 2022-06-30

This article introduces one more specific solution of the travelling salesman problem. The seller has to distribute, using his truck, goods from the depot (warehouse) to n customers. Each customer point of delivery is given by GPS coordinates. This problem can be called the travelling salesman problem. The objective of the solution is to select the sequence of delivery points so that firstly the travel distance and subsequently the total travel time are minimal. The seller visits all delivery points and returns to the depot. In this article, one general solution is presented using the bound-and-branche method and by using mixed integer linear programming implemented in Matlab code. The created algorithm can be used for any number n of customers.

CUBIC B-SPLINE LEAST SQUARES METHOD FOR THE NUMERICAL SOLUTION OF ADVECTION-DIFFUSION EQUATION

Idris Dag — 2022-06-30

Least squares algorithm is set up for getting solution of the time-dependent one-dimensional advection-diffusion equation (ADE). The cubic B-spline least squares method is coupled with the Crank-Nicolson scheme to produce the numerical method which is used to integrate the ADE fully. Two test problems are studied to illustrate the efficiency of the proposed method.