Sentence examples for by expressing the solution from inspiring English sources
By expressing the solution in terms of mid-surface variables, exact 2D equations are obtained for the rectangular interior plate.
This is done by expressing the solution as a sum of two linearly independent functions (the canonical functions) with specific values at some arbitrary point belonging to the interval defined by the two boundaries.
In [4], Khandaker and Raffoul studied the stability properties of the zero solution of the nonlinear Volterra discrete system x(n+1) = A(n)x(n) + sum_{s=0}^{n}B(n,s x s)+g bigl(n, x(n) bigr) by expressing the solution in terms of the resolvent matrix.
This can be captured by expressing the solution A of Equation 5.1 as a combination of a fixed wave profile A0 that is displaced by an amount Δ t) from its uniformly translating mean position ξ = x - ct, and a time-dependent fluctuation Φ in the front shape about the instantaneous position of the front: A ( x, t ) = A 0 ( ξ - Δ ( t ) ) + ε Φ ( ξ - Δ ( t ), t ).
Inversion is carried out by first expressing the solution of the direct problem formally in terms of the governing operators and making explicit approximations to these expressions.
Analytical solutions are obtained by expressing the material balances for each process as a first order, non linear difference equation.
The exact fundamental solutions could be found by expressing the coefficients of the reduced differential equation in a polynomial form before applying the Frobenius method.
Express the solution or project proposed by the group.
Thompson [5] investigated an essentially singular solution by expressing Feigenbaum's equation as a singular Schroder functional equation whose solution was obtained using a scaling ansatz, and so on.
