Convergence of Fixed Point Iteration Method.

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Rajkishor Patra (M.Sc Jadavpur University)
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Details explanation of Fixed Point Iteration Method(Convergence).(2nd Lecture)

Details explanation of Fixed Point Iteration Method(Algorithm).(1st Lecture).👇
   • Fixed Point Iteration Method or Metho...  
Details explanation on Bisection Method and its convergence, Advantages, and Disadvantages.(2nd Lecture of Bisection Method).👇
   • Bisection Method of Numerical Methods...  
(1St Lecture of Bisection Method)Bisection Method and its geographical representation.👇
   • Bisection Method of Numerical Methods...  
Second degree polynomial passes through (0,5),(2,7),(4,17),(6,35) is.👇
   • Second degree polynomial passes throu...  
Prove that u_0+x/1!u_1+x^2/2!+u_2+...=e^x[u_0+x∆u_0+x^2/2!∆^2u_0+...].👇
   • Prove that u_0+x/1!u_1+x^2/2!+u_2+......  
Prove that u_0+n_c_1u_1x+n_c_2u_3x^3+...=(1+x)^nu_0+(1+x)^(n-1)x∆u_0+(1+x)^(n-2)x^2∆^2u_0+...👇
   • Prove that u_0+n_c_1u_1x+n_c_2u_3x^3+...  
Prove that u_x-(1/8)∆^2u_(x-1)+(1.3/8.16)∆^4u_(x-2)-....=u_(x+1/2)-1/2∆u_(x+1/2)+....👇
   • Prove that u_x-(1/8)∆^2u_(x-1)+(1.3/8...  
If f_i is the value of f(x) at x=x_i, where x_i=x_0+ih, i=0,1,2,...n, prove that f(x)=Summation i=0 to n (-u)_c_i (nebla)^i f_n.👇
   • If f_i is the value of f(x) at x=x_i,...  
Prove of ∆^kf(x)=Summation i=0 to k(-1)^i(k_C_i)f[x+(k-i)h] Or ∆^ky_0=Summation i=0 to k(-1)^i(k_C_i)y_(k-i).👇
   • ∆^kf(x)=Summation i=0 to k(-1)^i(k_C_...  
Show that Summation x=0 to n=(n+1)_C_1 u_0+(n+1)_C_2∆ u_0+(n+1)_C_3∆^2 u_0+...+∆^nu_0 and hence find 1^3+2^3+....+n^3.👇
   • Show that Summation x=0 to n=(n+1)_C_...  
Prove of ∆n_C_(x+1)=n_C_x and Summation n=1 to N n_C_x=(N+1)_C_(x+1)-1_C_(x+1).👇
   • Prove that ∆n_C_(x+1)=n_C_x and Summa...  
Value of ∆^ncos(ax+b) and ∆^nsin(ax+b)👇
   • Value of ∆^ncos(ax+b) and ∆^nsin(ax+b)  
Prove of Nebla_(n+1)=h[1+1/2 nebla+5/12nebla^2+...]Dy_n, where D is differential operator. With explanation.👇
   • Nebla_(n+1)=h[1+1/2 nebla+5/12nebla^2...  
Prove of ∆^(n+1)f(x)=h^(n+1)f^(n+1)(x) if h is very small. With explanation.👇
   • ∆^(n+1)f(x)=h^(n+1)f^(n+1)(x) if h is...  
Prove of ∆^m(1/x)=(-1)^m(m!)h^m/x(x+h)(x+2h)...(x+mh). 👇
   • ∆^m(1/x)=(-1)^m(m!)h^m/x(x+h)(x+2h).....  
Prove of ∆logf(x)=log{1+∆f(x)/f(x)} with explanation.👇
   • ∆logf(x)=log{1+∆f(x)/f(x)}  
This is the 3rd Lecture (Part -B)of finite Difference.
Definition of shift Operator and Central difference averaging and derivation inter relation.👇
   • Difference Operators and their Inter ...  
This is the 3rd Lecture (Part -A)of finite Difference.
Definition of shift Operator and Central difference averaging and derivation inter relation.👇
   • Difference Operators and their Inter ...  
This is the 2nd Lecture of finite Difference.
Definition of shift Operator and Central difference averaging and derivation inter relation.👇
   • Forward, Backward, Shift, Central, Av...  

This is the 1st Lecture of finite Difference.
Definition of forward and backward difference and derivation inter relation.👇
   • Forward Difference and Backward Diffe...  

Given u=x^3y^3/2, if x_0,y_0 be the approximate value of x,y respectively and ∆x_0, ∆y_0 are the
absolute error in them. Determine the relative error.
   • Given u=x^3y^3/2, if x_0,y_0 be the a...  
If u=xyz+x^3 and error in x,y,z are 0.01, 0.025, 0.03 respectively at x=1, y=2 ,z=3, computing maximum value of absolute and relative error in evaluating u.
   • If u=xyz+x^3 and error in x,y,z are 0...  
Absolute and relative error on Fundamental Operations, Multiplication and Division.👇
   • Error on Fundamental Arithmetic Opera...  
Absolute and relative error on Fundamental Arithmetic Operations, Subtraction.👇
   • Error on Fundamental Arithmetic Opera...  
How to find absolute and relative error on Fundamental Arithmetic Operations, Addition.👇
   • Error on Fundamental Arithmetic Opera...  
How to estimate the error in general.👇
   • General Formula of Estimation of Erro...  
Solution of two important problem based on relative and percentage error.👇
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Relation between absolute error and decimal place with application.👇
   • Relation between Absolute Error and N...  
Relation between relative error and number of significant digits with application.👇
   • Relation between Relative Error and N...  
Maximum value of Absolute error.👇
   • Maximum value of Absolute Error if nu...  
Absolute, Relative and Percentage error. Exact number and approximate number.👇
   • Exact and Approximate Number. Absolut...  
Round off a number and rules of round off.👇
   • Rounding-off number. Rules of Roundin...  
Significant digits or figure and how to find the number of significant digits of a number.👇
   • Significant digits or Significant fig...  
Different sources of error in numerical method.👇
   • Sources of error  (1) Inherent error....