finite difference methods definitions. finite difference methods approximate derivatives **...
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Finite Difference Methods
Definitions
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Finite Difference MethodsApproximate derivatives
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** difference between exact derivative and its approximation is the truncation error
Finite Difference MethodsGiven a smooth function (i.e., a function that is continuous and has continuous derivatives), the Taylor series approximates the value of a function at one point based on the value of the function and its derivatives at another, nearby point
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Finite Difference MethodsFirst-order Taylor series:
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solving for the first derivative
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Finite Difference Methods
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Truncation error:
Finite Difference Methods
Exercise: write the Taylor series expansion for q(x - x) and solve for the first differential...
Finite Difference Methods
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Finite Difference Methods
Backward time difference: explicit
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Forward time difference: implicit
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