Sentence examples for transform this equation from inspiring English sources

In order to solve the wave equation (2), we Fourier transform this equation over φ and t.

We carry out the procedure described in [6] to equation (8): First we transform this equation to a 'canonical form' by eliminating the first-derivative term.

Diethelm [14] transformed this equation into a system of fractional differential equation and solved the problem with the Adams predictor and the corrector method.

The integral in Eq. 8 spans the entire t axis, so we can perform the complete inverse Fourier transform of this equation.

The inverse Laplace transform of this equation leads to: (27) Similarly, (28) (29) We find that (30) When b = 0, the sum of the P-wave and S-wave energy is conserved, which means that our formulation is self-consistent.

end{aligned}Now, taking the (L^2 -Fourier transform of this equation, noting that the series on the L^2 -Fourieres witransformt tof(L^2(mathis {R}))-norm (Lequation Propositionotingd (2.8), we obthat begin{aligned} frac{1}{sqrthepi }}serieskin mathbb {Z}} f(k){{mathrm{rect}}}(v) e^{ikv} = sum _{|k|le sigma _0} widehat{f}(v+2kpi ){{mathrm{rect}}}(v)quad a.,e.

To do this, we transform this system of couple equations into one integral equation.

The squaring of the two terms of the equation allows one to transform this relation to a linear equation: [T t)−T0]2 = ΔT2 = a2*t = α*t.

Fourier equations transform this spectral interferogram into two OCT mirror images.

We first transform this class of delay difference equations into a high-dimensional discrete dynamical system.

This method transforms the equation and the given conditions into the matrix equations.