Matrix-valued Bratu equationnormal modelexact solutionLie algebraA matrix-valued extension of the Bratu equation is defined. For its initial value problem, the exponential matrix solution and power series solution are provided.doi:10.1142/S2661335219500072Hiroto Inoue...
The new idea is to study the stability behavior of the solution x=x(t) x = x ( t ) mathContainer Loading Mathjax of the initial value problem x ˙ = Ax , t t 0 , x ( t 0 ) = x 0 mathContainer Loading Mathjax , with A∈C n×n A ∈ C n × n mathContainer Loading Ma...
Some modified matrix eigenvalue problems
Use the matrix exponential to solve the initial value problem. {eq}\displaystyle x' = \begin{bmatrix}-2 &2 \\1 &-3\end{bmatrix} x + \begin{bmatrix}0 \\1 \end{bmatrix};\ x (0) = \begin{bmatrix}1\\ 2 \end{bmatrix} {/eq} Solving matrix by ...
Answer to: Solve the given initial-value problem. x'=\begin{pmatrix} 4 &-1 \\ 5&2 \end{pmatrix}x,x(0)=\binom{-4}{8} x(t) = (___) By signing...
Two-Point Boundary Value Problem (TPBVP) Consider the autonomous equation x˙(t)=f(x) of order n. The trajectory x[t0, t) is the solution of an initial value problem when only the initial condition x(t0) is known as in Eq. (13.5). A more generic problem, known as TPBVP, occurs ...
If the regularization does not fix the problem for a pixel, the program would switch to the CED method. We call our strategy Combined eigenvalue maximum likelihood Phase Linking (CPL). 2.2.4 Short bandwidth This approach is a modified version of the phase linking method that uses a partial ...
The Asymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations as an Initial Value Problem for a First-Order Quasilinear Symmetr... The asymptotic characteristic initial value problem for Einstein's vacuum field equations where data are given on an incoming null hypersurface ...
Many scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are pr...
Solve the initial value problem {eq}{x}'=\begin{bmatrix} -2 & 1\\ -5&4 \end{bmatrix} {/eq}; {eq}x(0)=\begin{bmatrix} 1\\ 3 \end{bmatrix} {/eq} Solving a Linear System of a Real Matrix: The general solution of the linear hom...