Methods of Applied Mathematics

A₁ approximate solution augmented matrix boundary conditions c₁ c₂ calculation characteristic functions characteristic numbers characteristic values characteristic vectors coefficients column consider convergence coordinates corresponding characteristic deduce defined deflection denote determined diagonal difference equation differential equation dx dy elements end conditions Euler equation expressed Figure follows formula Fredholm equation function f(x given Green's function hence Hermitian homogeneous initial integral equation interval involved kernel Laplace's equation linear combination linearly independent method multiple notation notice obtained orthogonal orthogonal matrix positive definite possesses prescribed procedure ratio relation relevant replaced residual result of Problem right-hand member satisfies the equation Section set of equations sin² space square matrix Suppose symmetric matrix takes the form temperature tion transformation vanish variables verify y₁ Yk+1 λη λι дх Ук მყ