Numerical Methods for Solving Differential Equations

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In summary, the problem is about solving for velocity (v) at a given time (t) using numerical methods and differential equations. The equation (1) and a hint about using the substitution y=g-(c/m)v are provided. The solution involves moving the g-(c/m)v term to the dv side and integrating both sides. The hint also suggests using initial conditions, if given.
  • #1
CHRIS57
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Numerical Methods/Diff Eq :)

2. Problem

2cdizj9.jpg


Clarified: Solving for v(t)

Homework Equations



equation (1)

The Attempt at a Solution



I know the two parts of the hint are important, and tried moving the dt over to the other side and integrating, but I can't seem to isolate the velocity. I think I have to do a derivative before integrating, but I'm not sure how?Thanks guys ;)
 
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  • #2


Move the g-(c/m)v over to the dv side as well and integrate both sides. The equation is 'separable'. The hint is indicating that you then use the substitution y=g-(c/m)v on the dv side.
 
  • #3


Dick your answer is incredible, I've also been struggling with differential equations but now it makes a whole lot more sense haha

PS, mr. OP, are there any initial conditions given?
 

FAQ: Numerical Methods for Solving Differential Equations

What is the difference between numerical methods and analytical methods?

Numerical methods involve approximating solutions to mathematical problems using algorithms and computer calculations, while analytical methods involve finding exact solutions using mathematical equations and techniques.

What are some common applications of numerical methods in science?

Numerical methods are used in various fields of science, such as physics, engineering, and economics, to solve complex mathematical problems that cannot be solved analytically. Some common applications include modeling physical systems, predicting weather patterns, and analyzing financial data.

What is the role of differential equations in numerical methods?

Differential equations are used to model relationships between variables in many scientific problems. Numerical methods are then used to approximate the solutions to these equations, enabling researchers to make predictions and analyze the behavior of systems.

How do numerical methods help to improve accuracy in scientific calculations?

Numerical methods use iterative processes to refine and improve upon initial approximations, resulting in more accurate solutions. Additionally, numerical methods allow for the handling of complex and nonlinear systems that cannot be solved analytically.

What are some common challenges and limitations of using numerical methods?

Some challenges of using numerical methods include the potential for round-off errors, the need for careful selection of algorithms and parameters, and the trade-off between accuracy and computational efficiency. Additionally, numerical methods may not always provide exact solutions and may require a significant amount of computational resources.

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