Consider these two boundary-value problems: Show that if x is a solution of boundary-value problem,...
clear steps and brief explanation please
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Consider these two boundary-value problems: Show that if x is a solution of boundary-value problem,... clear steps and brief explanation please 7. Consider these two boundary-value problems: . x-f (t...
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value probl...
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
Prove that the following two-point boundary-value problem has a UNIQUE solution. Thank you Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
1. Second order linear boundary value problems: Discuss the solution process for a linear boundary value...
1. Second order linear boundary value problems: Discuss the solution process for a linear boundary value problem of the form u" (x) + g(x)u, (x) + h (x)u(x) = f(x), -u,(a) + u (a) = α, u,(b) + u(b) = β a. a < x < b where a, b E R with a < b, g(x), h(x) and f(x) are given functions, and α, β E R b. The funconsux) and u2(x) solve the differential equation u"(x) +g(x)u'(x) +...
This is PDE problem. Please show all steps in detail with neat handwriting. Problem . Consider...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2...
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
Please show full solution and explanation Consider the following two functions h (t) and f (t)....
Please show full solution and explanation
Consider the following two functions h (t) and f (t).
and
(a) Plot h(t) and f(t).
(b)Use the convolution integral to calculate the convolution g
(t) of the function h (t) with f (t) and plot.
So if t > 0 h(t) = 1 et if t > 0 Ji if 0 <t<T f(t) = 10 if otherwise
(b) Let f 0, 1-R be a C2 function and let g, h: [0, 00)-R be C1. Consider the initial-boundary value problem kwr w(...
(b) Let f 0, 1-R be a C2 function and let g, h: [0, 00)-R be C1. Consider the initial-boundary value problem kwr w(r, 0) f(a) w(0, t) g(t) w(1, t) h(t) for a function w: [0,1 x [0, 0)- R such that w, wn, and wa exist and are continuous. Show that the solution to this problem is unique, that is, if w1 and w2 [0, 1] x [0, 00)- R both satisfy these conditions, then w1 = w2....
7. Consider the boundary value problem for the Laplace equation on the strip u (0, y)...
7. Consider the boundary value problem for the Laplace equation on the strip u (0, y) u (т, y) = 0, = a. Explain why it makes sense to look for a solution of the form b. Find all solutions of the form u(x, y) -ZYn (v)sinnx satisfying c. Among the solutions you found in part (b) find the unique solution u (x, y)-Yn (y) sin n. the Laplace equation and the boundary conditions. (i.e. find Yn. (3).) that satisfies...
Let u be the solution to the initial boundary value problem for the Heat Equation, dụı(t, x)-20 1...
Let u be the solution to the initial boundary value problem for the Heat Equation, dụı(t, x)-20 11(t, x), IE(0, oo), XE(0,3); with initial condition u(0,x)-f (x), where f(0) 0 andf'(3)0, and with boundary conditions Using separation of variables, the solution of this problem is with the normalization conditions 3 a. (5/10) Find the functions wn, with index n 1. wn(x) = 1 . b. (5/10) Find the functions vn, with index n
Let u be the solution to the...
2. Show that the Dirichlet problem for the disc t(z,y): +y S R2), where f(0) is the boundary func...
use the hint please
2. Show that the Dirichlet problem for the disc t(z,y): +y S R2), where f(0) is the boundary function, has the solution 0o aj COS 1 sin j 3-1 where a, and b, are the Fourier coefficients of f. Show also that the Poisson integral formula for this more general disc setting is R22 (Hint: Do not solve this problem from first principles. Rather, do a change of variables to reduce this new problem to the...
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
1. Second order linear boundary value problems: Discuss the solution process for a linear boundary value problem of the form u" (x) + g(x)u, (x) + h (x)u(x) = f(x), -u,(a) + u (a) = α, u,(b) + u(b) = β a. a < x < b where a, b E R with a < b, g(x), h(x) and f(x) are given functions, and α, β E R b. The funconsux) and u2(x) solve the differential equation u"(x) +g(x)u'(x) +...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
Please show full solution and explanation
Consider the following two functions h (t) and f (t).
and
(a) Plot h(t) and f(t).
(b)Use the convolution integral to calculate the convolution g
(t) of the function h (t) with f (t) and plot.
So if t > 0 h(t) = 1 et if t > 0 Ji if 0 <t<T f(t) = 10 if otherwise
(b) Let f 0, 1-R be a C2 function and let g, h: [0, 00)-R be C1. Consider the initial-boundary value problem kwr w(r, 0) f(a) w(0, t) g(t) w(1, t) h(t) for a function w: [0,1 x [0, 0)- R such that w, wn, and wa exist and are continuous. Show that the solution to this problem is unique, that is, if w1 and w2 [0, 1] x [0, 00)- R both satisfy these conditions, then w1 = w2....
7. Consider the boundary value problem for the Laplace equation on the strip u (0, y) u (т, y) = 0, = a. Explain why it makes sense to look for a solution of the form b. Find all solutions of the form u(x, y) -ZYn (v)sinnx satisfying c. Among the solutions you found in part (b) find the unique solution u (x, y)-Yn (y) sin n. the Laplace equation and the boundary conditions. (i.e. find Yn. (3).) that satisfies...
Let u be the solution to the initial boundary value problem for the Heat Equation, dụı(t, x)-20 11(t, x), IE(0, oo), XE(0,3); with initial condition u(0,x)-f (x), where f(0) 0 andf'(3)0, and with boundary conditions Using separation of variables, the solution of this problem is with the normalization conditions 3 a. (5/10) Find the functions wn, with index n 1. wn(x) = 1 . b. (5/10) Find the functions vn, with index n
Let u be the solution to the...
use the hint please
2. Show that the Dirichlet problem for the disc t(z,y): +y S R2), where f(0) is the boundary function, has the solution 0o aj COS 1 sin j 3-1 where a, and b, are the Fourier coefficients of f. Show also that the Poisson integral formula for this more general disc setting is R22 (Hint: Do not solve this problem from first principles. Rather, do a change of variables to reduce this new problem to the...
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