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# Category Archives: Differential Equations

## 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
2 Comments

## 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
4 Comments

## 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
2 Comments

## 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

## Elegant solutions, Column buckling, and the hole through the middle of the Earth

The previous post presented some examples of solution of differential equations using an iterative process, including the simple harmonic motion problem of a ball falling through an evacuated hole through the middle of the Earth. The final example was concerned … Continue reading

Posted in Beam Bending, Differential Equations, Newton
Tagged column deflections, differential equations, Euler buckling
4 Comments