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amin, harahap
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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SIMPLIFIED FORMULAS FOR SOME BESSEL FUNCTIONS AND THEIR APPLICATIONS IN EXTENDED SURFACE HEAT TRANSFER Irvan, Irvan; Zahedi, Zahedi; Agus, Anjar; Suparni, Sarmin; Amin, Harahap
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (492.512 KB) | DOI: 10.30598/barekengvol16iss2pp507-514

Abstract

Bessel functions find many applications in Physics and Engineering fields. Some of these applications are in the analysis of extended surface heat transfer where the cross-sections vary. Tables of various kinds of Bessel functions are available in most handbooks of mathematics. However, the use of tables is not always convenient, particularly for applications where many values must be computed. In the applications of Bessel functions in extended surface heat transfer, graphs are also available to provide quick evaluations of the values needed. However, reading these graphs always needs interpolation; this will be cumbersome and time-consuming if there are many readings to be taken. Mathematical formulas for Bessel functions are available but they are usually complicated. Software to calculate values of Bessel functions is also available. Excel, Maple, and Mathematica can also be used to compute the values of Bessel functions. A user can write a program for an application that involves Bessel functions. However, the use of Bessel functions in Excel is limited while Maple and Mathematica are expensive commercial software. In this paper, formulas for Bessel functions of and are simplified with adequate accuracy that can be used to easily compute values needed in the extended surface heat transfer analysis. It is found that errors for and are relatively small (maximum errors are 0.004% and 0.003%, respectively) in the range of 0.05 to 3.75 while the maximum error for is 3.678% for the same range. However, the maximum error for is reduced to 0.166 if the range is from 0.25 to 3.75.
C PROGRAM AS A TOOL FOR THE TEACHING OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATION Amin, Harahap; -, Zahedi; Enos, Lolang; Ansoruddin, Ansoruddin; Wingkolatin, Wingkolatin; Efendi, Efendi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0205-0212

Abstract

Second order ordinary differential equation (ODE) has many applications in science and engineering. Undergraduate students in science and engineering departments must study this subject in order to understand other subjects which are related to real applications they will encounter later. There are many excellent textbooks on differential equations where the students can study the theory and solve the problems. However, a textbook cannot give a quick answer for a problem particularly when the problem is quite difficult. A good choice is to use software such as Maple or Mathematica. However, this software is not always available for the teaching and purchasing it is usually beyond the ability of a student or even a lecturer. On the other hand, lecturers who want to create problems by themselves will follow the theory of the ODE. While creating the problems may not be difficult, answering them are harder. Problems which are very easy to answer are less worthless because they will not increase the students’ knowledge. Here comes the solution. A C program has been created to help lecturers create problems and solve them quickly. The program is interactive and can be easily understood by anyone who has basic theory of ODE. No knowledge of programming is needed; a user just runs it and follows the instruction. Students can also use the program to sharpen their knowledge. They can compare the solution of a problem they have solved with the answer given by the program. While commercial software such as Maple and Mathematica is very powerful, they cannot be used without writing necessary commands to solve a problem.
Co-Authors -, Zahedi Agus, Anjar Ansoruddin, Ansoruddin Efendi Efendi Enos Lolang Irvan Irvan Suparni, Sarmin Wingkolatin, Wingkolatin Zahedi .