# Tagged Questions

Tag for the usage of RSolve, ReccurenceTable, and implementation of finite difference method(FDM) in Mathematica

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### Has this implementation of FDM touched the speed limit of Mathematica?

Still, I'll use the implementation of the 1D FDTD method (you can simply understand it as a kind of explicit finite difference scheme for the Maxwell's equation) as the example. Just for completeness, ...
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### Mathematica 9 cannot solve a difference equation that Mathematica 8 can

Consider RSolve[{a[n + 1] == 2 a[n] + n (1 + 2^n), a[1] == 1}, a[n], n] Mathematica 8 can solve this quickly, but Mathematica 9, even after being allowed to run ...
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### Kernel crash when evaluating NDSolveValue

I had a code that was working fine and I tried to add an extra few lines to find the solution of the same equation with different conditions. The original NDSolveValue solutions work fine but when it ...
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### Show Factorial instead of Gamma in the result of RSolve

Now I wanted to solve for a recurring function with RSolve. Here's how I tried: ...
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### Making a table or expression based on previous values

I would like to illustrate rational expectations based on the following equation p[[t+1]] == 1/(1 - ψ (β - 1)) m[[t+1]] - ψ (β - 1)/(1 - ψ (β - 1)) p[[t]] by ...
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### Finite Difference - heat generation in a square (square within a square)

I am trying to develop a code that will allow me to solve the following problem. Lets say that I have a square block, inside that square block I have a smaller square box thats at a certain ...
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### Random Variable in Recurrence Function

Following the previously published question, I'm looking for the solution of RecurrenceTable with explicit random variable. For example, something like ...
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### RecurrenceTable with a recurrence function of two variables

I have to calculate the cool down process of a regenerative heat exchanger. I solved the problem in Excel before, but now I want to do it with Mathematica. I want to create a table with the variables ...
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### Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way to get a formula for the nth term?
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### Computing a sequence by recurrence

I am trying to create a list where each element of the list is calculated using the sum of all previous elements of the list and also uses the $N$th element of another list. The initial value of the ...
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### Plotting logistic maps

I have a question about plotting in Mathematica in general, and this particular recurrence relation as an example: $\qquad x _{n+1} = rx_{n}(1-x_{n})$ How can I plot the following plots as shown ...
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### How to approximate the solution of a system of quartic equations

In an attempt to evaluate the point at which the cycle 2 becomes unstable for the given map: $$x_{n+1}=μ-x_n^4=f(x_n), \quad μ \in \mathbb{R}$$ I have so far managed to ...
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### How to solve coupled complex-valued equations faster and get simplified solution

I have six coupled equations. How to solve these equations symbolically faster in Mathematica. In these equations, variables p,q,x,y are ...
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### Permutations and recurrence equation

First problem: I need to show all Permutations with length 4 of this elements {x, y, z, w, t} but with this condition: the element z mustn't be after element t. I ...
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### Why does Mathematica not evaluate the difference recurrence using RSolve or RecurrenceTable?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
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### Speeding up a differential equation system with nested modulo periodic events

I have the following differential equation system with periodic Events : ...
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### RSolve and a recurrence relation

In the book An Introduction to the Analysis of Algorithms there is a recurrence relation for the number of compares used in Quicksort algorithm: $$C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1})$$ (...
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### Getting the first $n$ terms of a recursion relation

Given a recursion relation, I would like to generate the first $n$ terms (automatically) without having to go term by term. Background Each term is of the form $a_{n}(t)$, that is, $a_{n}$ is a ...
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### RSolve with conditional equation

I have the following conditional equation: $f(n) = 1+2 f(n/2)$ when n is even $f(n) = 1+f((n-1)/2)+f((n+1)/2)$ when n is odd I want to represent this as a conditional equation to be used in ...