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3. Construct the weak form of the following nonlinear equation: ( - «(1= v2
Question (2.5) In Problems 2.4-2.9, construct the weak forms and, whenever possible, the associated quadratic functionals (I). A linear differential equation: 2.4 du + u x dx dx du u(0) =1, dx =2 2.5 A nonlinear equation: du +f=0 for 0 <x<1 dx dx dx = 0 u(1)-V2 In Problems 2.4-2.9, construct the weak forms and, whenever possible, the associated quadratic functionals (I). A linear differential equation: 2.4 du + u x dx dx du u(0) =1, dx =2 2.5...
Construct the weak form and the finite element model of the following differential equation over a typical element Ω0€ (rf.xs). d ( du〉 , du dx dx)d Here a, b, and fare known functions of x and u is the dependent variable. The natural boundary conditions should not involve the function b(r). Construct the weak form and the finite element model of the following differential equation over a typical element Ω0€ (rf.xs). d ( du〉 , du dx dx)d Here...
2. Construct the weak form of the following linear equation. Are the boundary conditions “essential” or “natural”? Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0 Il (x +r) --sin (x ) OSxst dx du ax 11 (0)=0 =0
3. Express each of the following in simplified Cartesian form. a) (v2- V60)0 (V2 + V65)25 (b) 21010(-1 +)0(+) 4. Find the complex number z, in Cartesian form, such that it satisfies the equation 5. Find all solutions of the equation r 160 Express any complex solutions in Cartesian form, simplified as much as possible.
Construct a Liapunov function on the form V(x,y) = ax2 + cy2 for the nonlinear system dx dt dy dt 3 山 一一 and deduce that the critical point at the origin is asymptotically stable. Construct a Liapunov function on the form V(x,y) = ax2 + cy2 for the nonlinear system dx dt dy dt 3 山 一一 and deduce that the critical point at the origin is asymptotically stable.
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form y' + P(x)y = Q(x)yn that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is y1 − ne∫(1 − n)P(x) dx = (1 − n)Q(x)e∫(1 − n)P(x) dxdx+C (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) y8y' − 2y9 = exs
Please find V1 and V2 (in differential Equation form) in the following circuits 10 igtn Pytn) 2- Fitr) 3- btn igin Pitt) 1.
Question 1) (3 Points) Consider the strong form below. Derive the weak form equation. The space used is W H-1,1]. Define the spaces Wp and Wo Dirichlet Strong Form: Find u e W2,00 such that u"(x) _ 2 sin(x)a(z) u(-1)-1 u(1) 1 cos(x), for any x ? ?-[-1,1]
An exponential equation is a nonlinear regression equation of the form y= ab^x. Use technology to find and grab the exponential equation for the accompanying data, which shows the number of bacteria present after a certain number of hours. Include the original data in the graph. Note that this model can also be found by solving the equation log y= mx + b for y. Number of hours, x: 1 2 3 4 5 6 7 Number of bacteria, y:...
HW6. Please find v1 and V2 (in differential Equation form) in the following circuits: i1t0) 1200) Pi() M 1t0) 240) e2l0) 3- i1(0) 200) 1(0) e2l4) 4- 1(0) 200) ei(0) 02(1)