(1)u(r +h, t+ k) + u(x – h, t – k) = u(x+ k,t+ h) + u(x – k, t – h), 2) Consider the initial boundary value problems:{Ə?u – au = 0,u(х, 0) — 0,u(0, t) = 0,πε (0, π ) ,t> 0,дли (и, 0) — 1,u(T, t) = 0,6.x E (0, 7), initial data,t > 0, boundary values.%3D(a) Solve it using formula (1).(b) Is the resulting solution continuous? Is C1 i.e, u(, t) differentiablewith d;u(x, t), dqu(x,t) continuous?

Ques 2 a) Given equation is homogenous wave equation. utt-uxx=0with i.c. u(x,0)=0; ut(x,0)=1with…

2) Consider the initial boundary value problems: Ofu – azu = 0, u(п, 0) — 0, u(0, t) = 0, x E (0, 1), t > 0, дди (х, 0) — 1, u(T, t) = 0, x E (0, 7), initial data, t > 0, boundary values. (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C1 i.e, u(x, t) differentiable th ôu(x, t), Ôgu(x,t) continuous?

2) Consider the initial boundary value problems: Ofu – azu = 0, u(п, 0) — 0, u(0, t) = 0, x E (0, 1), t > 0, дди (х, 0) — 1, u(T, t) = 0, x E (0, 7), initial data, t > 0, boundary values. (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C1 i.e, u(x, t) differentiable th ôu(x, t), Ôgu(x,t) continuous?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Matrices And Determinants

Section6.4: Determinants And Cramer’s Rule

Problem 3E

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