To solve stiff coupled (simultaneous) ODEs,
one choice is Semi-implicit Euler method .
Is there fully implicit (i.e. not-semi) method for coupled ODEs ?
Or is there another good method ?
2026-04-28 11:19:11.1777375151
Implicit method for coupled ODEs
750 Views Asked by user357000 https://math.techqa.club/user/user357000/detail At
1
There are 1 best solutions below
Related Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
- Error Bound using Stirling's approximation
Related Questions in SYSTEMS-OF-EQUATIONS
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- System of equations with different exponents
- Is the calculated solution, if it exists, unique?
- System of simultaneous equations involving integral part (floor)
- Solving a system of two polynomial equations
- Find all possible solution in Z5 with linear system
- How might we express a second order PDE as a system of first order PDE's?
- Constructing tangent spheres with centers located on vertices of an irregular tetrahedron
- Solve an equation with binary rotation and xor
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
No, the semi-implicit or symplectic Euler method applies to Hamiltonian systems, not general stiff problems. And when you use it, go one step further and adapt the initial velocity so that the method becomes without further changes the leapfrog Verlet method.
Yes, there is an implicit Euler method. You will have to solve an equation system for the slope, for instance with Newton`s method. The implicit method with one Newton step is the simplest Rosenbrock method.
In general it makes no sense to use the order 1 Euler method when with essentially the same effort you could implement the order 2 midpoint method or the order 2 trapezoidal method.
And if the machinery is in place to deal with the equation system of implicit methods, you could just as well consider higher order methods, see for instance Butcher`s tutorial slides for his book, esp. the third set.