Poisson Equation Finite-Difference

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Poisson Equation Finite-Difference

• EXAMPLE 2
• Consider Poissons equation
• The boundary conditions
• Endpoint a0, b2, c0, d1
• Integers m5, n6
• Tolerance 10-10

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Poisson Equation Finite-Difference

• Main function

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Poisson Equation Finite-Difference
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Poisson Equation Finite-Difference

• Result

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Poisson Equation Finite-Difference

• Integers m5, n6
• Integers m10, n12

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Poisson Equation Finite-Difference

• EXERCISE
• Consider Poissons equation
• The boundary conditions
• Endpoint a0, b2, c0, d1
• Integers m10, n10
• Tolerance 10-10

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Poisson Equation Finite-Difference

• Result

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Heat Equation Backward-Difference

• EXAMPLE 2
• Backward-Difference method with h0.1 and k0.01
• Subject to the constrains
• Compare wi,50 to u(xi, 0.5)
• Endpoint l1
• Maximum time T0.5
• Constant a1
• Integers m10, n50

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Heat Equation Backward-Difference

• Main function

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Heat Equation Backward-Difference

• Result
• Integers m10, n50
• Integers m20, n100

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Crank-Nicolson Method

• Main function

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Crank-Nicolson Method

• Result

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Wave Equation Finite-Difference

• EXAMPLE
• Consider the hyperbolic problem
• boundary conditions
• Initial conditions
• Easily verified that the solution to this problem
• Endpoint l1
• Maximum time T1
• Constant a2
• Integers m10, N20

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Wave Equation Finite-Difference

• Main function

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Wave Equation Finite-Difference

• Result

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Wave Equation Finite-Difference

• EXERCISE
• Consider the hyperbolic problem
• boundary conditions
• Initial conditions
• Easily verified that the solution to this problem
• Endpoint l1
• Maximum time T1
• Constant a1
• Integers m4, N4

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Wave Equation Finite-Difference

• Result

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Finite-Element

• EXAMPLE
• Consider the problem
• boundary conditions
• Actual solution to the boundary-value problem

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Finite-Element

• Main function

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Finite-Element
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Finite-Element
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Finite-Element
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Finite-Element

• Result