Search results
3 days ago · In this paper, we consider numerical methods for the event location of differential algebraic equations. The event corresponds to cross a discontinuity surface, beyond which another differential algebraic equation holds. The methods are based on a particular change of the independent variable time, called time reparametrization or time transformation, reducing the equation to another equation ...
5 days ago · Now, by Newton’s second law, the sum of the forces on the system (gravity plus the restoring force) is equal to mass times acceleration, so we have. mx″ = − k(s + x) + mg = − ks − kx + mg. However, by the way we have defined our equilibrium position, mg = ks, the differential equation becomes. mx″ + kx = 0.
5 days ago · Problem-Solving Strategy: Finding Power Series Solutions to Differential Equations Assume the differential equation has a solution of the form \[y(x)=\sum_{n=0}^{\infty}a_nx^n. onumber \] Differentiate the power series term by term to get \[y′(x)=\sum_{n=1}^{\infty}na_nx^{n−1} onumber \]and\[y″(x)=\sum_{n=2}^{\infty}n(n−1)a_nx^{n− ...
2 days ago · Solving First Order ODEs. The Wolfram Language function DSolve finds symbolic solutions (that can be expressed implicitly or even explicitly) to certain classes of differential equations. The Wolfram Language function NDSolve, on the other hand, is a general numerical differential equation solver (it is discussed in more details in Part III ).
4 days ago · The Schrödinger equation is a linear differential equation, meaning that if two state vectors | and | are solutions, then so is any linear combination | ψ = a | ψ 1 + b | ψ 2 {\displaystyle |\psi \rangle =a|\psi _{1}\rangle +b|\psi _{2}\rangle }
5 days ago · Differential Scanning Calorimetry (DSC) is a thermoanalytical technique widely used in both research and industry to measure the amount of energy absorbed or released by a sample as it is heated, cooled, or held at a constant temperature. It is particularly useful in studying phase transitions, such as melting and crystallization, as well as ...
4 days ago · Solution of the above differential equation is done by separating both the variables on either side of the equal sign, dy/g (y) = dx/f (x) and then integrating them individually. This method of solving separable differential equations was first proposed by G. Leibniz in 1691 and was finalized by J. Bernoulli in 1694.
