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- ODE Solver Vs. Least Squares Curve Fit
ODE Solver 对比 Least Squares Curve Fit 的使用情况和统计数据
An ordinary differential equation or ODE is a differential equation containing a function or functions of one independent variable and its derivatives.
ODE Solver solves systems of ordinary equations with initial boundary conditions with 4th order Runge Kutta Method. It plots and lists results exporting them via email.
All variables, x, u, and t, should be entered with "$" prefix and ODE Solver does the rest.
Example: Typical Pendulum
dx/dt = $u
du/dt= -pi()**2/4*sin($x)-0.1*$u
Following functions are available in ODE Solver:
Operators:
+ add
- subtract
* multiply
/ divide
** pow exponentiation
Functions:
sqrt() - returns the square root of the passed parameter
log() - returns the base 10 log of the passed parameter
ln() - returns the base e log of the passed parameter
exp() - returns e raised to the power of the passed parameter
The trigonometric functions:
dtor() - converts the passed parameter from degrees to radians
rtod() - converts the passed parameter from radians to degrees
sin(), cos(), tan()
Their inverses (asin, acos, atan)
Their reciprocals (csc, sec, cotan)
The reciprocals of the inverses (acsc, asec, acotan)
The hyperbolic variations of all the above functions (sinh, cosh, tanh, asinh, acosh, atanh, csch, sech, cotanh, acsch, asech, acotanh)
Constants:
pi() - returns the value of π.
pi_2() - returns the value of π/2
pi_4() - returns the value of π/4
e() - returns the value of e
Other:
-Entry field background color turns to red color in case of unpaired parentheses and turns to green color once parentheses are paired again.
- Entry field background color turns to red colour in case of unpaired parentheses and turns to green color once parentheses are paired again.
- Recognizing entries with errors and raising warnings.
- Special keypad for formula entries.
- Cursor arrows enables editing entries.
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“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app.
User inputs point sets and chooses function types.
Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs.
Point sets can be stored in a table and are available after app is closed.
Currently available function types are:
2D:
1. Line.
2. Parabola.
3. Polynomial up to 8th degree.
4. Circle.
5. Conic section (Ellipse or Hyperbola).
6. Trigonometric function as
C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x),
where user can select n between 1 and 8 and enter any ω.
7. Exponential Function.
8. Bell Curve.
3D:
1. Plane.
2. Sphere.
Also, there is an option to choose the Best Fit:
the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals.
In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD.
Links to four other free apps by same developers are included in the app:
1. “Matrix Solver Step by Step” Linear Algebra Visual Guide.
2. “Polynomials and Linear Systems” Equation Solver.
3. “GraphMath” Graphing Calculator.
4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide.
Developers hope to get feedback from users at graphmath@aol.com.
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ODE Solver与Least Squares Curve Fit排名比较
对比 ODE Solver 与 Least Squares Curve Fit 在过去 28 天内的排名趋势
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ODE Solver 对比 Least Squares Curve Fit 的排名,按国家/地区比较
对比 ODE Solver 与 Least Squares Curve Fit 在过去 28 天内的排名趋势
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ODE Solver VS.
Least Squares Curve Fit
十二月 19, 2024