# Category Archives: Differential Equations

## 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 | | 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 | | 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 | | 5 Comments

## Using the AlgLib ODE (Runge-Kutta) Solver with Excel

Or to be more correct, the AlgLib Cash-Karp Solver, Cash-Karp being a refinement of the Runge-Kutta method of solving ordinary differential equations. Solution of differential equations is an iterative process requiring the repeated application of the solver routine followed by evaluation of … Continue reading

Posted in AlgLib, Beam Bending, Differential Equations, Excel, Maths, Newton, UDFs, VBA | | 8 Comments