Solve Troesch's Equation: Numerical Technique & Derivation

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In summary, Troesch's equation is a nonlinear differential equation commonly used in fluid mechanics, first derived by Swiss mathematician Georges Troesch in the 1940s. The most commonly used numerical technique to solve it is the shooting method, and it does not have a general analytical solution. The equation has applications in various fields, including fluid mechanics, heat transfer, and chemical engineering, and can be derived using a combination of dimensional analysis and the Navier-Stokes equations. It is often used as a simplified version of the full Navier-Stokes equations in certain fluid flow problems.
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Troesch's equation explanation
hi, i am going to solve Troesch's equation u′′(x) = λ sinh(λu(x))
by numerical technique, but i couldn't find the derivation of it- kindly anyone knows its derivation or details of variable used.
regards wasi
 
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Here is an introduction, a solution and a bibliography.
https://www.researchgate.net/publication/253644077_A_general_solution_for_Troesch's_problem/link/55a9969208ae815a04254f47/download
 
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FAQ: Solve Troesch's Equation: Numerical Technique & Derivation

What is Troesch's equation?

Troesch's equation is a nonlinear differential equation that describes the behavior of a fluid flow through a porous medium. It is commonly used in the study of fluid dynamics and has applications in various fields such as geology, engineering, and environmental science.

What is the numerical technique used to solve Troesch's equation?

The most commonly used numerical technique to solve Troesch's equation is the finite difference method. This method involves approximating the derivatives in the equation using a finite set of points and then solving the resulting system of algebraic equations.

What is the derivation of Troesch's equation?

Troesch's equation can be derived from the Navier-Stokes equations, which describe the motion of a fluid. It involves assuming a simplified form of the Navier-Stokes equations for a fluid flow through a porous medium and applying the Darcy's law to account for the porous nature of the medium.

What are the boundary conditions for solving Troesch's equation?

The boundary conditions for solving Troesch's equation depend on the specific problem being studied. However, in general, the boundary conditions include specifying the fluid velocity at the inlet and outlet of the porous medium, the pressure at the boundaries, and any other relevant physical parameters.

What are some applications of solving Troesch's equation?

Troesch's equation has various applications in the fields of geology, engineering, and environmental science. It is commonly used to model fluid flow in porous media, such as groundwater flow in aquifers, oil flow in reservoirs, and air flow in soils. It can also be used to study the transport of contaminants in groundwater and the behavior of pollutants in soil and sediment systems.

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