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6. The simulation of parameter-distributed processes is connected with discretization in space and time. The distribution of changes in the temperature x of a heated at the front massive long metal piece is described by the following partial differential equation: ax(z,t) at fð²x(z,t) dz² (1) = -a(x-0₂)+b where 0, is the ambient temperature, a and b are constants. Derive the discrete model by applying discretization first with respect to z (z;= i.Az) and after that with respect to t (tk=k.At), using backward finite differences for the corresponding derivatives.

6. The simulation of parameter-distributed processes is connected with discretization in space and time. The distribution of changes in the temperature x of a heated at the front massive long metal piece is described by the following partial differential equation: ax(z,t) at fð²x(z,t) dz² (1) = -a(x-0₂)+b where 0, is the ambient temperature, a and b are constants. Derive the discrete model by applying discretization first with respect to z (z;= i.Az) and after that with respect to t (tk=k.At), using backward finite differences for the corresponding derivatives.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Revert Don. 6. The simulation of parameter-distributed processes is connected with discretization in space and time. The distribution of changes in the temperature x of a heated at the front massive long metal piece is described by the following partial differential equation: a²x(z,t) Oz² ax(z,t) (1) = -a(x-0₂)+b at where 0, is the ambient temperature, a and b are constants. Derive the discrete model by applying discretization first with respect to z (z;= i.Az) and after that with respect to t (tk=k.At), using backward finite differences for the corresponding derivatives.
Transcribed Image Text:Revert Don. 6. The simulation of parameter-distributed processes is connected with discretization in space and time. The distribution of changes in the temperature x of a heated at the front massive long metal piece is described by the following partial differential equation: a²x(z,t) Oz² ax(z,t) (1) = -a(x-0₂)+b at where 0, is the ambient temperature, a and b are constants. Derive the discrete model by applying discretization first with respect to z (z;= i.Az) and after that with respect to t (tk=k.At), using backward finite differences for the corresponding derivatives.
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