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Category Archives: Differential Equations
xlwSciPy update for Python 3
The xlwSciPy spreadsheet allows a wide variety of the science and maths functions in the Python Numpy and Scipy libraries to be called directly from Excel. The spreadsheet has now been updated for use with Python 3. The spreadsheet and … Continue reading
Posted in Coordinate Geometry, Differential Equations, Excel, Link to Python, Maths, Newton, Numerical integration, NumPy and SciPy, Python Pandas, UDFs, VBA, xlwings
Tagged Excel, Numpy, Python, SciPy, UDF, VBA, xlwings
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Rabbits, Foxes, and Lorenz Attractors
Following comments here and here I have added two examples to the ODE Solver spreadsheet showing use of the ODE function to solve systems of differential equations with two or more coupled equations. The new version (including full open source … Continue reading
Posted in AlgLib, Differential Equations, Excel, Maths, Newton, UDFs, VBA
Tagged AlgLib, Excel, Lorenz Attractor, Predator-Prey, Solution of ODEs, Systems of ODEs, UDF, VBA, XNumbers
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Daily Download 21: Assorted Solvers
Today’s download starts with some simple linear interpolation methods used to solve polynomial equations, leading on to more sophisticated methods using quadratic or inverse quadratic interpolation. Also included is a solver for differential equations using the Cash-Karp Method, which is … Continue reading
The hole through the middle of the Earth – filled with air
Three air molecules go into a hole, Well, I say three; could have been four or five. Could have been nine or ten, doesn’t matter. Could have been fifteen, twenty – fifty. Round it up. Hundred. Let’s go mad, eh … Continue reading
Posted in AlgLib, Differential Equations, Excel, Maths, Newton, UDFs, VBA
Tagged big numbers, Excel, hole through the middle of the earth, ODE Function, Perfect gas, UDF, VBA
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The hole through the middle of the Earth – moved to the Equator
Previous posts in this series assumed that the hole went from pole to pole, and ignored such complications as tidal effects and wobbles of the axis of rotation. In this post we will examine the effect of moving the hole … Continue reading
Posted in Differential Equations, Excel, Maths, Newton, UDFs, VBA
Tagged Excel, hole trough the middle of the Earth, ODE Function, ODE solver, UDF, VBA
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The hole through the middle of the Earth – revised transit time
In the previous post in this series I produced a table of acceleration due to gravity against depth from surface, based on the four layers of the Earth (Crust, Mantle, Outer Core, Inner Core), assuming a constant density for each layer. … Continue reading
Posted in Differential Equations, Excel, Newton, UDFs, VBA
Tagged Excel, hole through the middle of the earth, ODE Function, UDF, VBA
3 Comments
The hole through the middle of the Earth – acceleration
In my first go at modelling a ball falling through a hole through the middle of the Earth I assumed constant density, and hence the acceleration at any point was proportional to the distance from the centre. That is of course … Continue reading
