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The spatial domain, 0≤ x≤ L x, is discretised uniformly with grid spacing δ x, and the spatial derivatives are approximated using a central-difference approximation [ 40].

Each scale variable is approximated using a meshfree method.

The POF is approximated using a quintic polynomial.

This function is approximated using a truncated complex Fourier series.

Irrational numbers (like pi or e or sqrt(2)) are instead approximated using a finite binary expansion.

The solution of the Fokker Planck equation is approximated using a reduced basis spectral method.

Furthermore, in past work the necessary third order derivatives are approximated using a finite different approach.

This relationship can be approximated using a slightly modified van Genuchten function.

Therefore, in our previous work, the crack shape was approximated using a planar parametrized representation.

Away from the curve, the original subdivision surfaces are approximated using a multi-resolution scheme based on quasi-interpolation.

The performance of the heat pipe drill model is approximated using a solid cylinder model of pure conduction.

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