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MATRICES AND DETERMINANTS
MATHEMATICAL MODELING OF TYPICAL ENGINEERING
SIMULTANEOUS LINEAR ALGEBRAIC EQUATIONS
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applied assumed augmented matrix backward boundary conditions calculated characteristic equation Clearly coefficient matrix column computed Consequently Consider the following constant corresponding Cramer's rule data points deflection derivative approximations determined diagonal displacement easily eigenproblem eigenvalues eigenvector engineering equal evaluated evident example finite difference finite element method following set functional values Furthermore given by equation gives Hence increment initial conditions integration interpolating function interpolating polynomial interval inverse iterations Jacobi method linear algebraic equations mathematical model multiplying nodes nonlinear Note numerical methods objective function obtained Obviously ordinary differential equations partial derivatives partial differential equations procedure reducing matrix Rework problem root Runge-Kutta method second derivative second-order polynomial set of equations set of linear shown in figure Simplifying Solve the following Substituting equation Substituting into equation symmetrical matrix Taylor series techniques tion transformed trapezoidal rule unknowns vector yields zero