Consider the pure advection equation: du +5=0; 0x 1; u(x,0) = sin(x); u(0,t) = 0...

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Consider the pure advection equation: ди du +5=0; 0≤x≤ 1; u(x,0) = sin(x); u(0,t) = 0 Ət Consider the following finite difference approximation: (n+1) 5At ) = u(") - 5 (u(") - u")), where the standard notation used in class for time-marching is introduced. Superscript n is used to denote time index (i.e. at t(n) and t(n+1)) whereas subscript i is used to denote the space index x, and ₁-1. (a) [1 point] Is this an explicit method or an implicit method? (b) [2 points] Using positivity of coefficients, find any restrictions on the step sizes. Show all steps. Consider the pure advection equation: ди du +5=0; 0≤x≤ 1; u(x,0) = sin(x); u(0,t) = 0 Ət Consider the following finite difference approximation: (n+1) 5At ) = u(") - 5 (u(") - u")), where the standard notation used in class for time-marching is introduced. Superscript n is used to denote time index (i.e. at t(n) and t(n+1)) whereas subscript i is used to denote the space index x, and ₁-1. (a) [1 point] Is this an explicit method or an implicit method? (b) [2 points] Using positivity of coefficients, find any restrictions on the step sizes. Show all steps. Consider the pure advection equation: ди du +5=0; 0≤x≤ 1; u(x,0) = sin(x); u(0,t) = 0 Ət Consider the following finite difference approximation: (n+1) 5At ) = u(") - 5 (u(") - u")), where the standard notation used in class for time-marching is introduced. Superscript n is used to denote time index (i.e. at t(n) and t(n+1)) whereas subscript i is used to denote the space index x, and ₁-1. (a) [1 point] Is this an explicit method or an implicit method? (b) [2 points] Using positivity of coefficients, find any restrictions on the step sizes. Show all steps. Consider the pure advection equation: ди du +5=0; 0≤x≤ 1; u(x,0) = sin(x); u(0,t) = 0 Ət Consider the following finite difference approximation: (n+1) 5At ) = u(") - 5 (u(") - u")), where the standard notation used in class for time-marching is introduced. Superscript n is used to denote time index (i.e. at t(n) and t(n+1)) whereas subscript i is used to denote the space index x, and ₁-1. (a) [1 point] Is this an explicit method or an implicit method? (b) [2 points] Using positivity of coefficients, find any restrictions on the step sizes. Show all steps.

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The given finite difference approximation is as follows uin1 uin 5tx uin ui1n where uin denotes the ... View the full answer