The Fourth Order Runge-Kutta Spreadsheet Calculator Using VBA Programing for Ordinary Differential Equations

Tay, Kim Gaik; Kek, Sie Long; Han, Cheong Tau; Abdul-Kahar, Rosmila; Lee, Ming Foong

doi:10.1016/j.sbspro.2015.08.145

Cited by 10 publications

(9 citation statements)

References 1 publication

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“…Runge-Kutta fourth-order algorithm was adopted to solve the involved differential equations owing to its high accuracy for such equations [30,36], assuming a linear variation over a small time step of 0.001 s. The LCRB properties such as K b and C b , and u y were calculated based on following equations [37]:…”

Section: Solution Methodsmentioning

confidence: 99%

Effects of Building Height and Seismic Load on the Optimal Performance of Base Isolation System

Dushimimana

Mbereyaho

et al. 2023

Arab J Sci Eng

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Seismic isolation has been widely accepted as one of the techniques that can be used to protect structures during earthquake ground motions. However, some challenges still exist such as the optimal control of excessive isolator shear strains imposed by some ground motions. The main purpose of this study was to assess the effects of building height variation and earthquake ground motion type on the optimal performance of the seismic isolation using lead core rubber bearing (LCRB). Nonlinear time history analysis for building models of various storeys isolated by LCRB and exposed to different real earthquakes was performed. To achieve this, the equations governing the motion of the isolated three different building models were presented, and an approach for solving the equations while taking into consideration of the optimized mechanical properties of the LCRB was developed. The LCRB performance was measured in terms of elastomer shear strains, derived after an optimal criterion leading to reliable substructure and superstructure responses was reached. The results showed that the combined effects of the earthquake type and building height significantly affect the substructure responses (maximum isolator displacement, energy dissipation capacity, maximum isolator force) and the superstructure responses (storey shear forces, storey drifts, floor displacements, and floor accelerations), which in some cases lead to a need for adding a fluid damper. In this regard, an attempt to couple the LCRB with nonlinear fluid viscous damper was made, and the performance of the hybrid was assessed. It was generally found that the hybrid can positively improve the substructure responses, thereby reducing the unwanted large elastomer shear strains without adversely affecting the superstructure responses.

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Section: Solution Methodsmentioning

confidence: 99%

Effects of Building Height and Seismic Load on the Optimal Performance of Base Isolation System

Dushimimana

Mbereyaho

et al. 2023

Arab J Sci Eng

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“…The mathematical functions explain the many basic terminologies of electrical concepts particularly those of voltage, current, resistance and graphical representations, elaborating processes based on the spreadsheet [2], [3], [4] operations. The main focus of this paper is to highlight the mathematical basis of electrical models that regulate the operation of spreadsheets in Microsoft Excel [3], [3], [5], [6], [7]. The spreadsheet application is among the most widely used computing tools in modern society because it is not possible to solve these equations analytically, so numerical solution is mandatory, there are numerous numerical methods available to solve odes [8], [9], [10], [11], among all the methods 5 t h order Runge-Kutta method (RK5) [12], [13], [14], [15] is interesting.…”

Section: Introductionmentioning

confidence: 99%

A Higher Order Runge-Kutta Method for Solving System of Ordinary Differential Equations Using MS Excel

Shaikh

2021

QUESTRJ

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The differential equations, solved numerically, are often implemented on simulation and computational tools. This requires programming skills. Excel spreadsheet has been used frequently for statistical analysis, however it is rarely used for computation in mathematics, instead of having great usability and usefulness. It also easily enables a non-programmer to perform programming-like tasks in a visual tabular pen and paper approach. Many physical phenomena are modelled in terms of odes and PDEs, so solving these types of equations, by cooperative iterative methods, are very important there are several iterative methods. The Euler and Runge-Kutta are the most famous ones among the numerical methods for solving the differential equations as well as system(s) of the differential equation(s). Euler's method has slow convergence; therefore, methods of a higher order of accuracy are often needed. Since the iterative methods manually with pen-paper are quite tedious and laboring because it involves numerous repetitive calculations. The spreadsheet technique in Excel is in cooperated to solve the system of an ode by applying the RK5 methods, but one of the pitfalls of an excel spreadsheet is that it is limited containing less than 256 variables (columns) and 65536 records (rows).

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“…The most simple and widely used method reported for simulating different physical problems is based on spreadsheets. Numerous reports in the literature have been devoted to the use of spreadsheets for solving and understanding different problems in physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Simulating longitudinal vibrations of coupled oscillator using the fourth-order Runge–Kutta method by programming spreadsheet

Singh¹,

Kaur²,

Khun³

2019

Eur. J. Phys.

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This paper presents a simple way of simulating the motion of two oscillators coupled via springs. A linear model using Hooke’s law describes the motion of a coupled oscillator through a set of two coupled second-order linear differential equations. A spreadsheet is programmed to obtain the numerical solutions of coupled differential equations using the fourth-order Runge–Kutta method. The main thrust behind programming the spreadsheet is to solve the differential equations for a physical system under different initial condition and to understand the motion of coupled masses graphically. The programmed spreadsheet can also be modified to include damping in the system and visualize a damped dynamical system. The algorithm developed for programming presents the use of inbuilt functions of the spreadsheet and is user-friendly, especially for those who are not familiar with the spreadsheets. Simulations of the coupled oscillator would help students to visualize the effect of variation of different parameters, such as mass, initial velocity, spring constant, and damping factor, on the motion of coupled oscillators.

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The Fourth Order Runge-Kutta Spreadsheet Calculator Using VBA Programing for Ordinary Differential Equations

Cited by 10 publications

References 1 publication

Effects of Building Height and Seismic Load on the Optimal Performance of Base Isolation System

Effects of Building Height and Seismic Load on the Optimal Performance of Base Isolation System

A Higher Order Runge-Kutta Method for Solving System of Ordinary Differential Equations Using MS Excel

Simulating longitudinal vibrations of coupled oscillator using the fourth-order Runge–Kutta method by programming spreadsheet

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