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3answers
256 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
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0answers
114 views

Smooth Max and Abs

I'm trying to implement smooth approximations of Max and Abs functions. Moreover I want the functions to map element-wise on tensors. Here's my code. ...
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0answers
55 views

Decimal representations of analytic values in an expansion

I have a solution to an ODE (which I call sol), which I would like to expand in terms of Log[1+x] around x=-1. I thought that: ...
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0answers
42 views

Approximate a function of four variables with a rational polynomial

I have a function that consists of four variables. Currently, I want to view it as function of one variable over the interval (0, 1) with the other three variables as parameters. I will plug values ...
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0answers
37 views

How do I estimate the Pareto front in my multiobjective optimization problem?

I need to minimize a function of two parameters that gives two "stress" outputs {A,B} = f[tau,mu]. How do I estimate (even roughly), the Pareto front for this ...
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0answers
38 views

How to approximate a computationally expensive 5-dimensional manifold?

I have a 4-parameter family of functions, which I'll refer to as y[a, b, c, d][x]. In this notation, a, b, c, d are the 4 ...
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0answers
33 views

Formulas for combining ChebyshevT coefficients?

I have two 5th-order (6th-order?) Chebyshev approximations: f1[x_] = Sum[a[n]*ChebyshevT[n,x],{n,0,5}] f2[x_] = Sum[b[n]*ChebyshevT[n,x],{n,0,5}] and f1[1] == ...
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0answers
97 views

Compute coefficient of Generating function

Given a generating function $F(z)$, is there any way to compute the coefficient $a_k$ of $z^k$ by Mathematica? One method is to calculate by the equation $\frac{F^{(k)}(0)}{k!}$. However, this ...