ODEcalc 6.71 ... Problem-Solving Application #2

ODEcalc (tm): an ODE Calculator!
Solves IVP & BVP with ODEs.

An Ordinary Differential Equation (ODE) Calculator! State your equation with boundary or initial value conditions and ODEcalc will solve your problem. Plots solution (y) and derivative (ydot) versus x. Solves most Boundary Value Problems (BVP) & Initial Value Problems (IVP) for any order ODE. ODE may be non-linear, implicit, and any order. Source code included ... it's short! ODEcalc helps one understand difference in BVP & IVP and their importance in solving practical differential equations. PDEs, ODEs and algebraic system of equations may be solved using the methodology in this demo. Great for learning BVP & IVP solution techniques. Solvers used are based on Automatic Differential (AD) and Operator Overload techniques.

Anyone seeking an Online math tutor?

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I specialize in solving Differential Equations (DEs) or systems. DEs may be explicit or implicit. There is an App, ODEcalc, on my website that is free and may be of help solving an ODE for you. Phil Brubaker tutors Differential Equations and other App usage or modification of my Apps OnLine via Zoom from Roseburg, OR. He has a Bachelor degree in Math with a Minor in Electrical Engineering. Tutoring fee is $10/h. Contact Phil now!

ODEcalc 6.71 Source code:

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ODEcalc was made possible due to a Calculus compiler. The source code (ODE4user.fc) file is included in order to show the Calculus programming simplicity. ODEcalc was written to show that differential equations are solved without numerical algorithms from the user. Differential equation problems are solved with little code other than ones equations. One initial value problem required only 19 lines of code in order to be solved! ODEcalc is a free (3.5 MB) download.

ODEcalc 6.71 Output Plots:

(Click Any Image To Enlarge)

ODE Solution Y & Ydot Curve Plots

CurvFit: a curve fitting program with Lorentzian, Sine, Exponential and Power series are available models to match your data.

Match-n-Freq: a Matched Filter program used to filter signals and slim pulses.

Business Strategies & War Gaming: Buy, Sell, Hold options may be tested for an entire company, individual plant(s), or whole product lines. Imagine an increase in control settings from a 1 or 2 digits (i.e., a guess value) to an 8+ digit accuracy resulting from a Calculus programming calculation!

Pulse Slimming to minimize InterSymbol Interference: via Arbitrary Equalization with Simple LC Structures to reduce errors.

Voice Coil Motor: basically an electromagnetic transducer in which a coil placed in a magnetic pole gap experiences a force proportional to the current passing through the coil.

Electrical Filter Design: find the transfer function's poles & zeros; H(s) = Y_out(s) / Y_in(s).

Digitized Signal from Magnetic Recording: Magnetic recording of transitions written onto a computer disc drive may produce an isolated pulse as shown.

AC Motor Design: a simulation program for A.C. motor design that was reapplied as a constrained optimization problem with 12 unknown parameters and 7 constraints.

PharmacoKinetics: an open-two- compartment model with first order absorption into elimination from central compartment is presented here.

Calculus (level) Problem-Solving for Engineers & Scientists

Textbooks - Parameter Estimation 4 ODE/PDE - Signal Analysis / Spectral Estimation - Body Plasma - Solar Cell
Increasing Productivity Examples: AC Motor Design - Matched Filters - Pulse Slimming / InterSymbol Interference - Pilot (safe) Ejection - PharmacoKinetics Simulation - Business Strategies & War Gaming - BVP - Implicit Equations